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Законы масштабирования дистилляции

Рекомендация для читателей:


Прежде чем погрузиться в детали, советую ознакомиться с двумя отличными статьями инженера из Яндекса (статья 1, статья 2). В них отлично объясняются принципы дистилляции, её применение в промышленных задачах и ключевые практические аспекты. Это идеальный старт для тех, кто только начинает знакомиться с темой.

Однако, если вы, как и я, стремитесь к глубокому пониманию — этого может оказаться недостаточно. В данном обзоре мы пойдём дальше:

  1. Математическая формализация: Разберём более глубако уравнения, лежащие в основе дистилляции, включая функцию потерь с температурным параметром, оптимизацию распределений и законы масштабирования из работы Apple.

  2. Примеры кода: Покажем, как реализовать дистилляцию на практике — от простых моделей на PyTorch до тонкой настройки гиперпараметров.

  3. Нюансы исследований: Ответим на вопросы, оставшиеся за рамками вводных материалов. Например, почему «слишком умный учитель» вредит ученику и как математически обосновать оптимальное соотношение их размеров.

Для кого это?
Если вы хотите не просто использовать дистилляцию «из коробки», а понимать, как и почему она работает — этот разбор для вас. Мы заглянем «под капот» методов, чтобы вы могли осознанно применять их в своих проектах.

Part 1: Knowledge Distillation

Knowledge Distillation (Дистилляция знаний) — это метод обучения моделей-студентов (обычно меньшего размера и менее сложных) путем передачи "знаний" от предварительно обученной модели-учителя (обычно большей и более сложной). Основная идея заключается в том, что модель-учитель, обладающая большей емкостью и обученная на большом объеме данных, может передать не только свои "жесткие" предсказания (например, класс объекта), но и более богатую информацию о распределении вероятностей классов, которую модель-студент может использовать для более эффективного обучения.

Teacher и Student модели:

В парадигме Knowledge Distillation участвуют две основные модели:

  • Teacher (Учитель): Это большая, предварительно обученная модель, которая считается "экспертом" в решении определенной задачи. Учитель уже достиг высокой точности и обладает "знаниями", которые мы хотим передать студенту. Математически учитель представляется как функцияp(y∣x), которая для входных данных xx выдает распределение вероятностей pпо классам y.

  • Student (Студент): Это меньшая, более простая модель, которую мы хотим обучить. Цель студента — научиться имитировать поведение учителя, чтобы достичь сравнимой производительности, но при этом быть более эффективной с точки зрения вычислительных ресурсов, памяти или времени инференса. Студент представляется как функция q_θ​(y∣x), где θ— параметры модели, которые мы оптимизируем в процессе обучения.

Функция потерь (Loss Function) в Knowledge Distillation:

Общая цель Knowledge Distillation — минимизировать разницу между предсказаниями учителя и студента. Это формализуется через функцию потерьL, которая зависит от предсказаний учителяp(y|x) и студента q_{\theta}(y|x). Процесс обучения заключается в поиске оптимальных параметров $\theta$ для студента, которые минимизируют эту функцию потерь:

L(p(y|x), q_{\theta}(y|x)) \rightarrow \min_{\theta}

Это общее выражение, и конкретный вид функции потерь и способ дистилляции определяют различные подходы. Рассмотрим два основных подхода: hard-label и soft-label дистилляцию.

Это общее выражение, и конкретный вид функции потерь и способ дистилляции определяют различные подходы. Рассмотрим два основных подхода: hard-label и soft-label дистилляцию.

Hard-label Distillation для GPT моделей: объяснение на пальцах

Представьте, что у нас есть две модели:

  • Учитель (Teacher): Большая, мощная GPT модель, например, GPT-3 или что-то подобное. Она обладает огромным количеством знаний о языке и мире, и способна генерировать очень качественный и связный текст.

  • Студент (Student): Маленькая, более компактная GPT модель, например, уменьшенная версия GPT или Transformer меньшего размера. Она менее ресурсоемкая, но изначально уступает учителю в качестве генерации текста.

Наша цель - "научить" маленькую модель-студента генерировать текст так же хорошо, как и большая модель-учитель, используя метод Hard-label Distillation.

Шаги Hard-label Distillation в этом контексте:

  1. Генерация "жестких" меток учителем (Большой GPT):

    • Мы берем большой набор текстовых данных (например, обучающую выборку, на которой изначально обучался учитель, или просто большой корпус текстов).

    • Для каждого фрагмента текста (или запроса) из этого набора, мы просим большую модель-учителя сгенерировать текст. В контексте GPT, это означает, что мы подаем учителю входной текст (например, начало предложения или запрос) и просим его сгенерировать продолжение.

    • Учитель генерирует последовательность токенов, которые он считает наиболее вероятными для продолжения данного текста. Эти сгенерированные последовательности токенов и являются нашими "жесткими" метками.

    Пример:

    • Входной текст (запрос): "Столица Франции - это"

    • Учитель (Большая GPT) генерирует: "Париж." (токены: "Па", "ри", "ж", ".")

    • "Жесткая" метка: Последовательность токенов: ("Па", "ри", "ж", ".")

    Мы повторяем этот процесс для большого количества различных входных текстов, получая набор пар: (исходный входной текст, "жесткая" метка - последовательность токенов, сгенерированная учителем).

  2. Обучение студента (Маленький GPT) на "жестких" метках:

    • Теперь у нас есть синтетический датасет, состоящий из пар (исходный входной текст, "жесткая" метка). Мы будем использовать этот датасет для обучения маленькой модели-студента.

    • Мы обучаем студента предсказывать "жесткие" метки, сгенерированные учителем, используя стандартную задачу языкового моделирования. Это означает, что для каждого входного текста мы хотим, чтобы студент генерировал последовательность токенов, максимально похожую на "жесткую" метку, сгенерированную учителем.

    • В процессе обучения мы используем функцию потерь кросс-энтропии. Мы сравниваем распределение вероятностей токенов, предсказанное студентом, с "жесткой" меткой (которая по сути является распределением, где вероятность "правильного" токена равна 1, а всех остальных - 0). Мы стремимся минимизировать эту кросс-энтропию, заставляя студента "подражать" учителю в предсказании токенов.

    В нашем примере, если студент на вход "Столица Франции - это" предсказывает, например, "Лондон", то функция потерь будет высокой, так как "жесткая" метка учителя была "Париж". В процессе обучения студент будет корректировать свои параметры, чтобы в будущем для аналогичных запросов предсказывать "Париж" или что-то очень похожее на предсказание учителя.

Почему маленькая модель может предсказывать те же токены, что и большая?

  • Передача знаний через "жесткие" метки: Хотя Hard-label Distillation и теряет часть информации из распределения вероятностей учителя, она все равно эффективно передает ключевые знания о том, какие токены являются наиболее вероятными в определенных контекстах. Большая модель, будучи хорошо обученной, "знает", какие продолжения текста являются грамматически правильными, семантически уместными и стилистически подходящими. Генерируя "жесткие" метки, она как бы "подсказывает" маленькой модели, какие именно токены нужно предсказывать.

  • Фокус на наиболее важной информации: "Жесткие" метки концентрируются на наиболее вероятных токенах. В языковом моделировании часто бывает так, что для многих контекстов есть один или несколько доминирующих "правильных" продолжений. Hard-label Distillation помогает маленькой модели быстро освоить эти наиболее важные закономерности, игнорируя менее значимые детали, которые могут быть избыточными для достижения хорошего качества генерации.

  • Упрощение задачи обучения: Обучение на "жестких" метках превращает дистилляцию в стандартную задачу обучения с учителем. Это упрощает процесс обучения и позволяет использовать хорошо известные методы и оптимизаторы. Маленькой модели не нужно пытаться воспроизвести все тонкости распределения вероятностей учителя, ей достаточно научиться предсказывать наиболее вероятные токены, что является более простой задачей.

Важно отметить ограничения Hard-label Distillation:

  • Потеря "мягкой" информации: Как и указано в тексте, Hard-label Distillation теряет информацию о вероятностях других классов и "мягких" отношениях между классами. В контексте языковых моделей это означает, что студент может не улавливать все нюансы стиля, семантики и разнообразия, которые присутствуют в распределении вероятностей учителя. Например, учитель может знать, что "Париж" является самым вероятным ответом на "Столица Франции - это", но также понимать, что "Рим" или "Берлин" являются менее вероятными, но все же допустимыми ответами в определенных контекстах. Hard-label Distillation фокусируется только на "Париже", игнорируя эту "мягкую" информацию.

  • Потенциальное ухудшение разнообразия: Из-за фокусировки на "жестких" метках, студент может стать менее разнообразным в своих генерациях, чем учитель. Он может слишком точно копировать наиболее вероятные ответы учителя, упуская возможность генерировать альтернативные, но все еще качественные варианты.

Математическая формализация:

1. Генерация "жестких" меток учителем: Для каждого примераx^{(n)}из обучающей выборки, учительp(y|x)предсказывает распределение вероятностей классов. "Жесткая" меткаy^{(n)}выбирается как класс с максимальной вероятностью, предсказанной учителем. В контексте языков моделей, гдеyпредставляет собой последовательность токенов, учитель генерирует последовательность "жестких" метокy^{(1)}, \ldots y^{(N)}дляNпримеров. Здесьy^{(n)} = (y_1^{(n)}, \ldots, y_{T_n}^{(n)})представляет собой последовательность токенов длинойT_n.

y^{(1)}, \ldots y^{(N)} \sim p(y|x)

В более простом варианте, для классификации, y^{(n)} = \arg\max_{y} p(y|x^{(n)}). В случае последовательностей, учитель может генерировать целые последовательности наиболее вероятных токенов.

2. Обучение студента на "жестких" метках: Студентq_{\theta}(y|x)обучается максимизировать логарифмическую вероятность "жестких" меток, сгенерированных учителем. Это стандартная задача обучения с учителем, где целевыми метками являютсяy^{(1)}, \ldots y^{(N)}. Функция потерь, которую мы минимизируем (или эквивалентно, максимизируем отрицательную потерю), представляет собой ожидание логарифмической вероятности "жестких" меток под распределениемp(y|x)учителя.

\mathbb{E}_{p(y|x)} [\log q_{\theta}(y|x)] \rightarrow \max_{\theta}

В практической реализации, это ожидание аппроксимируется эмпирическим средним по обучающей выборке. Для последовательностей текста, функция потерь выглядит следующим образом:

\frac{1}{N} \sum_{n=1}^{N} \sum_{t=1}^{T_n} \log q_{\theta}(y_t^{(n)}|y_{<t}^{(n)})

Здесь:

* N — количество примеров в обучающей выборке.

* T_n — длина последовательности для $n$-го примера.

* y_t^{(n)} —t-й токен в последовательности "жестких" меток дляn-го примера, сгенерированных учителем.

* y_{<t}^{(n)} = (y_1^{(n)}, \ldots, y_{t-1}^{(n)}) — префикс последовательности доt-го токена.

* q_{\theta}(y_t^{(n)}|y_{<t}^{(n)}) — вероятность предсказания студентомt-го токенаy_t^{(n)} при условии предыдущих токеновy_{<t}^{(n)}, параметризованная\theta.

Эта функция потерь представляет собой кросс-энтропию между распределением "жестких" меток, сгенерированных учителем, и предсказаниями студента. Мы стремимся максимизировать эту величину, что эквивалентно минимизации отрицательной логарифмической правдоподобности или кросс-энтропии.

Преимущества и недостатки Hard-label Distillation:

  • Преимущества: Простота реализации и понимания. Можно использовать стандартные методы обучения с учителем.

  • Недостатки: Потеря информации, содержащейся в распределении вероятностей учителя. "Жесткие" метки содержат только информацию о наиболее вероятном классе, игнорируя вероятности других классов и "мягкие" отношения между классами, которые учитель "знает". Это может ограничить эффективность передачи знаний.

Реализация Hard-label Distillation на основе Open R1

Ниже представлена реализация Hard-label Distillation с использованием подхода, применяемого в проекте Open R1. Процесс разделен на два этапа: генерация данных учителем и обучение ученика.

@misc{openr1,
    title = {Open R1: A fully open reproduction of DeepSeek-R1},
    url = {https://github.com/huggingface/open-r1},
    author = {Hugging Face},
    month = {January},
    year = {2025}
}

Этап 1: Генерация "жестких" меток большой моделью (учителем)

import argparse
from datasets import load_dataset
from typing import Optional, Dict, Any

from distilabel.pipeline import Pipeline
from distilabel.models import vLLM
from distilabel.steps.tasks import TextGeneration

def build_hard_label_pipeline(
    teacher_model: str,
    base_url: str = "http://localhost:8000/v1",
    prompt_column: Optional[str] = None,
    prompt_template: str = "{{ instruction }}",
    temperature: float = 0.0,
    max_new_tokens: int = 4096,
    input_batch_size: int = 32,
) -> Pipeline:
    """
    Description:
    ---------------
        Создает конвейер для генерации "жестких" меток с использованием модели-учителя.

    Args:
    ---------------
        teacher_model: Идентификатор модели-учителя
        base_url: URL сервера vLLM
        prompt_column: Имя колонки в датасете, содержащей входные тексты
        prompt_template: Шаблон для форматирования промптов
        temperature: Температура для генерации (0.0 для "жестких" меток)
        max_new_tokens: Максимальное количество генерируемых токенов
        input_batch_size: Размер батча для входных данных

    Returns:
    ---------------
        Настроенный конвейер Distilabel

    Raises:
    ---------------
        Exception: В случае ошибки настройки конвейера

    Examples:
    ---------------
        >>> pipeline = build_hard_label_pipeline("deepseek-ai/DeepSeek-R1")
        >>> pipeline.run(dataset)
    """
    # Настраиваем параметры генерации с temperature=0 для получения детерминированных ответов
    generation_kwargs: Dict[str, Any] = {
        "max_new_tokens": max_new_tokens,
        "temperature": temperature,
        "top_p": 1.0,
        "do_sample": False,          # Отключаем семплирование для получения "жестких" меток
    }

    with Pipeline(
        name="hard-label-distillation",
        description="Конвейер для генерации 'жестких' меток с использованием модели-учителя",
    ) as pipeline:
        # Настраиваем модель-учителя через vLLM
        teacher = vLLM(
            model=teacher_model,
            tokenizer=teacher_model,
            extra_kwargs={
                "tensor_parallel_size": 1,               # Можно увеличить для больших моделей
                "max_model_len": max_new_tokens + 2048,  # Добавляем запас для контекста
            },
            generation_kwargs=generation_kwargs,
        )

        # Настраиваем шаг генерации текста
        text_generation = TextGeneration(
            llm=teacher,
            template=prompt_template,
            num_generations=1,           # Для "жестких" меток нам нужна только одна генерация
            input_mappings={"instruction": prompt_column} if prompt_column is not None else {},
            input_batch_size=input_batch_size,
        )

    return pipeline

def generate_hard_labels(
    dataset_name: str,
    dataset_split: str = "train",
    teacher_model: str = "deepseek-ai/DeepSeek-R1",
    output_dataset: str = "my-username/hard-label-distill-dataset",
    prompt_column: str = "problem",
    prompt_template: str = "You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}: {{ instruction }}",
    max_examples: Optional[int] = None,
    private: bool = False,
) -> Any:
    """
    Description:
    ---------------
        Генерирует "жесткие" метки с использованием модели-учителя и сохраняет результаты как набор данных на HuggingFace Hub.

    Args:
    ---------------
        dataset_name: Имя исходного датасета
        dataset_split: Имя сплита датасета
        teacher_model: Модель-учитель для генерации "жестких" меток
        output_dataset: Имя выходного датасета на HuggingFace Hub
        prompt_column: Имя колонки, содержащей входные данные
        prompt_template: Шаблон для форматирования промптов
        max_examples: Максимальное количество примеров для обработки
        private: Приватный ли выходной датасет

    Returns:
    ---------------
        Датасет с "жесткими" метками

    Raises:
    ---------------
        Exception: В случае ошибки генерации меток

    Examples:
    ---------------
        >>> hard_label_dataset = generate_hard_labels("my-dataset", "train")
        >>> hard_label_dataset.push_to_hub("my-username/hard-label-dataset")
    """
    # Загружаем исходный датасет
    print(f"Загрузка датасета '{dataset_name}' (сплит: {dataset_split})...")
    dataset = load_dataset(dataset_name, split=dataset_split)

    # Ограничиваем количество примеров, если указано
    if max_examples is not None and max_examples < len(dataset):
        dataset = dataset.select(range(max_examples))

    print(f"Создание конвейера для генерации 'жестких' меток с использованием {teacher_model}...")
    pipeline = build_hard_label_pipeline(
        teacher_model=teacher_model,
        prompt_column=prompt_column,
        prompt_template=prompt_template,
    )

    print(f"Запуск конвейера для генерации 'жестких' меток на {len(dataset)} примерах...")
    # Генерируем "жесткие" метки
    hard_label_dataset = pipeline.run(dataset=dataset)

    # Сохраняем результаты на HuggingFace Hub
    if output_dataset:
        print(f"Сохранение результатов в '{output_dataset}'...")
        hard_label_dataset.push_to_hub(output_dataset, private=private)
        print(f"Датасет с 'жесткими' метками успешно сохранен в '{output_dataset}'.")

    return hard_label_dataset

if __name__ == "__main__":
    parser = argparse.ArgumentParser(description="Генерация 'жестких' меток с использованием модели-учителя")
    parser.add_argument("--dataset", type=str, required=True, help="Имя исходного датасета")
    parser.add_argument("--split", type=str, default="train", help="Сплит датасета")
    parser.add_argument("--teacher-model", type=str, default="deepseek-ai/DeepSeek-R1", help="Модель-учитель")
    parser.add_argument("--output-dataset", type=str, required=True, help="Имя выходного датасета")
    parser.add_argument("--prompt-column", type=str, default="problem", help="Колонка с входными данными")
    parser.add_argument("--prompt-template", type=str,
                       default="You will be given a problem. Please reason step by step, and put your final answer within \\boxed{}: {{ instruction }}",
                       help="Шаблон для форматирования промптов")
    parser.add_argument("--max-examples", type=int, default=None, help="Максимальное количество примеров")
    parser.add_argument("--private", action="store_true", help="Сделать выходной датасет приватным")

    args = parser.parse_args()

    generate_hard_labels(
        dataset_name=args.dataset,
        dataset_split=args.split,
        teacher_model=args.teacher_model,
        output_dataset=args.output_dataset,
        prompt_column=args.prompt_column,
        prompt_template=args.prompt_template,
        max_examples=args.max_examples,
        private=args.private,
    )

Этап 2: Обучение модели-ученика на "жестких" метках

import logging
import os
import sys
from dataclasses import dataclass, field
from typing import Optional, Dict, Any

import datasets
import torch
import transformers
from datasets import load_dataset
from transformers import AutoTokenizer, set_seed
from transformers.trainer_utils import get_last_checkpoint

from trl import SFTTrainer, ModelConfig, TrlParser, get_peft_config
from open_r1.configs import SFTConfig
from open_r1.utils.wandb_logging import init_wandb_training

logger = logging.getLogger(__name__)

@dataclass
class HardLabelDistillConfig(SFTConfig):
    """Конфигурация для обучения ученика с использованием Hard-label Distillation."""

    dataset_name: str = field(
        default=None, metadata={"help": "Датасет с 'жесткими' метками, сгенерированными учителем"}
    )
    input_column: str = field(
        default="problem", metadata={"help": "Колонка с входными данными"}
    )
    target_column: str = field(
        default="generation_0", metadata={"help": "Колонка с выходными данными (жесткими метками) учителя"}
    )
    max_seq_length: int = field(
        default=2048, metadata={"help": "Максимальная длина последовательности"}
    )

def train_student_model(config: HardLabelDistillConfig, model_args: ModelConfig) -> None:
    """
    Description:
    ---------------
    Обучает модель-ученика на 'жестких' метках, сгенерированных учителем.

    Args:
    ---------------
        config: Конфигурация обучения
        model_args: Конфигурация модели

    Returns:
    ---------------
        None

    Raises:
    ---------------
        Exception: В случае ошибки обучения модели

    Examples:
    ---------------
        >>> train_student_model(config, model_args)
    """
    # Настраиваем логирование
    logging.basicConfig(
        format="%(asctime)s - %(levelname)s - %(name)s - %(message)s",
        datefmt="%Y-%m-%d %H:%M:%S",
        handlers=[logging.StreamHandler(sys.stdout)],
    )
    log_level = config.get_process_log_level()
    logger.setLevel(log_level)
    datasets.utils.logging.set_verbosity(log_level)
    transformers.utils.logging.set_verbosity(log_level)

    # Устанавливаем сид для воспроизводимости
    set_seed(config.seed)

    # Проверяем наличие последнего чекпоинта
    last_checkpoint: Optional[str] = None
    if os.path.isdir(config.output_dir):
        last_checkpoint = get_last_checkpoint(config.output_dir)
        if last_checkpoint is not None:
            logger.info(f"Найден чекпоинт, продолжаем обучение с {last_checkpoint}")

    # Инициализируем Weights & Biases, если нужно
    if "wandb" in config.report_to:
        init_wandb_training(config)

    # Загружаем датасет с 'жесткими' метками
    logger.info(f"Загрузка датасета с 'жесткими' метками: {config.dataset_name}")
    dataset = load_dataset(config.dataset_name)

    # Подготавливаем входные данные и метки для обучения
    def prepare_dataset(examples: Dict[str, Any]) -> Dict[str, Any]:
        """Форматирует данные для обучения с учителем."""
        return {
            "input_ids": examples[config.input_column],
            "labels": examples[config.target_column],
        }

    # Трансформируем датасет
    dataset = dataset.map(prepare_dataset, batched=True)

    # Загружаем токенизатор
    tokenizer = AutoTokenizer.from_pretrained(
        model_args.model_name_or_path,
        revision=model_args.model_revision,
        trust_remote_code=model_args.trust_remote_code,
    )

    # Настраиваем chat_template, если указан
    if config.chat_template is not None:
        tokenizer.chat_template = config.chat_template

    # Настраиваем параметры модели
    torch_dtype = (
        model_args.torch_dtype if model_args.torch_dtype in ["auto", None] else getattr(torch, model_args.torch_dtype)
    )
    model_kwargs: Dict[str, Any] = dict(
        revision=model_args.model_revision,
        trust_remote_code=model_args.trust_remote_code,
        torch_dtype=torch_dtype,
        use_cache=False if config.gradient_checkpointing else True,
    )
    config.model_init_kwargs = model_kwargs

    # Создаем SFT тренер
    trainer = SFTTrainer(
        model=model_args.model_name_or_path,
        args=config,
        train_dataset=dataset["train"],
        eval_dataset=dataset["validation"] if "validation" in dataset and config.eval_strategy != "no" else None,
        processing_class=tokenizer,
        peft_config=get_peft_config(model_args),
    )

    # Запускаем обучение
    logger.info("Начало обучения модели-ученика...")
    checkpoint: Optional[str] = None
    if config.resume_from_checkpoint is not None:
        checkpoint = config.resume_from_checkpoint
    elif last_checkpoint is not None:
        checkpoint = last_checkpoint

    train_result = trainer.train(resume_from_checkpoint=checkpoint)
    metrics = train_result.metrics
    trainer.log_metrics("train", metrics)
    trainer.save_metrics("train", metrics)
    trainer.save_state()

    # Сохраняем модель
    logger.info(f"Сохранение модели в {config.output_dir}")
    trainer.save_model(config.output_dir)

    # Создаем карточку модели и загружаем на HuggingFace Hub, если нужно
    kwargs: Dict[str, Any] = {
        "dataset_name": config.dataset_name,
        "tags": ["hard-label-distillation", "open-r1"],
    }

    if trainer.accelerator.is_main_process:
        trainer.create_model_card(**kwargs)
        # Восстанавливаем кэш для быстрого инференса
        trainer.model.config.use_cache = True
        trainer.model.config.save_pretrained(config.output_dir)

    # Оцениваем модель, если нужно
    if config.do_eval and "validation" in dataset:
        logger.info("Оценка модели...")
        metrics = trainer.evaluate()
        trainer.log_metrics("eval", metrics)
        trainer.save_metrics("eval", metrics)

    # Загружаем модель на HuggingFace Hub, если нужно
    if config.push_to_hub:
        logger.info("Загрузка модели на HuggingFace Hub...")
        trainer.push_to_hub(**kwargs)

if __name__ == "__main__":
    # Создаем парсер аргументов
    parser = TrlParser((HardLabelDistillConfig, ModelConfig))
    config, model_args = parser.parse_args_and_config()

    # Запускаем обучение
    train_student_model(config, model_args)

Пример использования

# Этап 1: Генерация "жестких" меток с использованием модели-учителя
python hard_label_distill.py \
  --dataset AI-MO/NuminaMath-TIR \
  --teacher-model deepseek-ai/DeepSeek-R1 \
  --output-dataset username/hard-label-math-dataset \
  --prompt-column problem

# Этап 2: Обучение модели-ученика на сгенерированных "жестких" метках
accelerate launch --config_file=recipes/accelerate_configs/zero3.yaml train_student.py \
  --model_name_or_path Qwen/Qwen2.5-1.5B-Instruct \
  --dataset_name username/hard-label-math-dataset \
  --input_column problem \
  --target_column generation_0 \
  --learning_rate 1.0e-5 \
  --num_train_epochs 2 \
  --packing \
  --max_seq_length 4096 \
  --per_device_train_batch_size 8 \
  --gradient_accumulation_steps 4 \
  --gradient_checkpointing \
  --bf16 \
  --output_dir models/Qwen2.5-1.5B-Hard-Label-Distill

II. Soft-label Distillation: Дистилляция с использованием "мягких" меток

Концепция:

Soft-label distillation, предложенная Хинтоном и соавторами в их знаменитой статье "Distilling the Knowledge in a Neural Network" (2015), является более совершенным методом дистилляции знаний. В отличие от Hard-label distillation, этот подход использует не только "жесткие" метки, но и полное распределение вероятностей, предсказанное учителем, в качестве "мягких" меток (soft labels).

"Мягкие" метки содержат значительно больше информации, чем "жесткие", поскольку они отражают уверенность учителя в различных классах и отношения между ними. Например, учитель может предсказать для изображения собаки вероятности [0.8 для "собака", 0.15 для "волк", 0.03 для "лиса", 0.02 для других классов]. Эта информация гораздо богаче, чем просто метка "собака".

Ключевым компонентом метода является "temperature scaling" (масштабирование температуры), который делает распределение вероятностей более "мягким" и информативным путем деления логитов модели на параметр температуры T > 1.

Soft-label Distillation для GPT моделей: объяснение на пальцах

Представьте, что у нас есть две модели:

  • Учитель (Teacher): Большая, мощная GPT модель с 175 миллиардами параметров. Она обладает глубоким пониманием языка и мира.

  • Студент (Student): Компактная GPT модель с 1.5 миллиардами параметров. Намного быстрее и экономичнее, но изначально уступает учителю в качестве.

Наша цель - научить студента генерировать текст так же хорошо, как учитель, используя Soft-label Distillation.

Шаги Soft-label Distillation:

  1. Генерация "мягких" меток учителем:

    • Для запроса "Столица Франции - это" большая модель-учитель не просто выдает "Париж", но вычисляет вероятности для всех возможных следующих токенов:

      • "Париж": 0.92

      • "город": 0.03

      • "Рим": 0.01

      • ... (и тысячи других токенов с малыми вероятностями)

    • Проблема: это распределение слишком "острое" - один токен имеет почти всю вероятность. Чтобы извлечь больше полезных знаний, применяем temperature scaling:

    • Делим логиты на температуру T (например, T = 2.0) перед применением softmax:

      • "Париж": 0.70 (уменьшилось с 0.92)

      • "город": 0.08 (увеличилось с 0.03)

      • "Рим": 0.05 (увеличилось с 0.01)

      • ... (другие токены тоже получают больше вероятности)

    • Эти "смягченные" распределения сохраняют намного больше информации о том, что модель-учитель "знает".

  2. Обучение модели-студента:

    • Студент обучается не только предсказывать правильный токен, но и воспроизводить всё распределение вероятностей учителя.

    • Для этого используется КЛ-дивергенция (или кросс-энтропия) между распределениями учителя и студента.

    • Важно: распределение студента также "смягчается" с той же температурой T для сопоставимости.

    • Функция потерь умножается на T² для компенсации уменьшения градиентов.

  3. Комбинированное обучение:

    • Обычно используется комбинация двух функций потерь:

      • α · (Потери от "мягких" меток) + (1-α) · (Стандартные потери от "жестких" меток)

    • Где α - коэффициент, обычно от 0.5 до 0.9

Почему это работает лучше Hard-label Distillation?

  • "Темные знания" (Dark Knowledge): Как назвал Хинтон, относительные вероятности "неправильных" ответов содержат ценную информацию. Например, если модель путает "собаку" с "волком", но не с "самолетом", это важная информация.

  • Передача неопределенности: Студент учится не только правильным ответам, но и тому, в каких случаях стоит сомневаться.

  • Более богатый сигнал: Вместо одного бита информации на каждый пример (правильный/неправильный класс), студент получает информацию о всем распределении вероятностей.

Математическая формализация:

1. "Мягкие" метки учителя с температурой T:

Еслиz_i- логит для класса (токена)iот учителя, то "мягкая" метка с температурой T:

p_i^T = \frac{\exp(z_i/T)}{\sum_j \exp(z_j/T)}

Разберем каждый элемент формулы:

* p_i^T: Это "мягкая" вероятность дляi-го токена, с учетом температурыT. Именно это распределение вероятностей, сгенерированное учителем, мы будем использовать как "мягкую метку".

* z_i: Это логит (logit) дляi-го токена, выданный моделью-учителем. Логиты - это значения, которые модель выдает перед применением функции softmax. Они представляют собой "сырые" оценки того, насколько модель уверена в каждом токене. Чем больше логит, тем больше уверенность модели в этом токене.

* T: Это параметр температуры (temperature). Как мы разбирали уже выше, температура используется для "смягчения" распределения вероятностей.

* \exp(x): Это экспоненциальная функцияe^x.

* \sum_j \exp(z_j/T): Это сумма экспоненциальных значений логитов, деленных на температуру, для всех возможных токеновj. Эта сумма используется для нормализации, чтобы вероятности в итоге суммировались к 1.

Пошаговое объяснение:

1. Деление логитов на температуруz_i/T: Когда мы делим логиты на температуруT > 1, мы уменьшаем абсолютные значения логитов.

2. Экспоненцирование\exp(z_i/T): Экспоненциальная функция преобразует логиты в положительные значения.

3. Нормализация\frac{\exp(z_i/T)}{\sum_j \exp(z_j/T)}: Деление на сумму экспоненциальных значений всех логитов гарантирует, что полученные значенияp_i^T будут представлять собой вероятностное распределение, то есть будут неотрицательными и в сумме дадут 1. Это стандартная операция softmax, но с применением температуры.

Интуиция и эффект температуры:

* При высокой температуре (например, T = 2.0), распределение вероятностей становится более "мягким" или "ровным". Вероятности для менее вероятных токенов увеличиваются, а вероятность наиболее вероятного токена уменьшается. Это позволяет "вытащить" больше информации из распределения, включая "темные знания" о менее вероятных, но все же релевантных вариантах.

* При низкой температуре (приближающейся к T = 1.0, или даже меньше), распределение становится более "острым". Вероятность наиболее вероятного токена приближается к 1, а вероятности остальных токенов стремятся к 0. При T=1 это стандартный softmax. ПриT \rightarrow 0 распределение становится дельта-функцией, выбирая только токен с наибольшим логитом.

Figure_1.jpg
Figure_1.jpg

2. Аналогично для студента:

q_i^T = \frac{\exp(z_i^q/T)}{\sum_j \exp(z_j^q/T)}

гдеz_i^q - логит студента для классаi.

Аналогия с формулой учителя: Эта формула абсолютно идентична формуле для учителя, за исключением того, что здесь используются логиты, выданные моделью-студентом.

* q_i^T: "Мягкая" вероятность дляi-го токена, сгенерированная студентом с температуройT.

* z_i^q: Логит дляi-го токена, выданный моделью-студентом.

* Цель: Мы применяем ту же температуруT к распределению студента, чтобы сделать его сопоставимым с "мягкими" метками учителя. Это необходимо для корректного расчета функции потерь дистилляции.

3. Функция потерь для Soft-label Distillation:

L_{soft} = T^2 \cdot \text{KL}(p^T || q^T) = T^2 \cdot \sum_i p_i^T \log\frac{p_i^T}{q_i^T}

МножительT^2 компенсирует уменьшение градиентов из-за temperature scaling.

Разберем компоненты:

* L_{soft}: Функция потерь Soft-label Distillation. Это значение, которое мы хотим минимизировать в процессе обучения студента.

* T^2: Квадрат температуры. Этот множитель используется для масштабирования функции потерь и компенсации уменьшения градиентов, вызванного температурой.

* \text{KL}(p^T || q^T): KL-дивергенция ( Kullback-Leibler divergence) между распределением учителя $p^T$ и распределением студентаq^T.

* \sum_i p_i^T \log\frac{p_i^T}{q_i^T}: Это развернутая формула KL-дивергенции для дискретных распределений.

Пошаговое объяснение KL-дивергенции:

1. \frac{p_i^T}{q_i^T}: Отношение вероятности учителя к вероятности студента для каждого токенаi. Если студент предсказывает вероятностьq_i^T близкую к вероятности учителяp_i^T, это отношение будет близко к 1.

2. \log\frac{p_i^T}{q_i^T}: Логарифм этого отношения. Если отношение близко к 1, логарифм будет близок к 0. Еслиq_i^Tсильно отличается отp_i^T, логарифм будет иметь большее абсолютное значение (отрицательное, еслиq_i^T > p_i^T, и положительное, еслиq_i^T < p_i^T).

3. p_i^T \log\frac{p_i^T}{q_i^T}: Умножение наp_i^T взвешивает вклад каждого токена в общую дивергенцию. Токены, которые учитель считает более вероятными (высокоеp_i^T), вносят больший вклад в функцию потерь.

4. \sum_i p_i^T \log\frac{p_i^T}{q_i^T}: Суммирование по всем токенамi дает общую KL-дивергенцию. KL-дивергенция измеряет "расстояние" между двумя распределениями вероятностей. В контексте дистилляции, она измеряет, насколько распределение студентаq^T отличается от распределения учителяp^T.

РольT^2:

* Применение температурыT "смягчает" распределения, что может привести к уменьшению величины градиентов при обучении. Умножение наT^2 масштабирует функцию потерь, чтобы компенсировать это уменьшение и сделать градиенты более значимыми, особенно на ранних этапах обучения. Это эмпирическая коррекция, которая помогает стабилизировать и ускорить обучение.

* ЦельL_{soft}: МинимизируяL_{soft}, мы заставляем распределение вероятностей студентаq^T максимально приблизиться к распределению вероятностей учителяp^T. Студент учится не только предсказывать "правильный" токен, но и имитировать всю "манеру мышления" учителя, выраженную в распределении вероятностей.

4. Комбинированная функция потерь:

L = \alpha \cdot L_{soft} + (1-\alpha) \cdot L_{hard}

гдеL_{hard} - стандартная кросс-энтропия с истинными метками,\alpha - коэффициент баланса.

Разберем компоненты:

* L: Общая функция потерь, используемая для обучения студента.

* \alpha: Коэффициент баланса (обычно от 0.5 до 0.9). Он определяет, насколько сильно мы полагаемся на "мягкие" метки учителя по сравнению со стандартными "жесткими" метками.

* L_{soft}: Функция потерь Soft-label Distillation, которую мы разобрали выше.

* L_{hard}: Стандартная функция потерь "жестких" меток, обычно кросс-энтропия между предсказаниями студента и истинными (one-hot) метками.


L_{hard} (Стандартные потери "жестких" меток):

* В обычной задаче обучения языковой модели, мы имеем "жесткие" метки - это истинные следующие токены в обучающих данных. Например, для фразы "Столица Франции - это Париж", "Париж" является "жесткой" меткой.

* L_{hard} вычисляется как кросс-энтропия между распределением вероятностей, предсказанным студентом (обычно сT=1, то есть стандартный softmax), и one-hot вектором, представляющим истинный токен. Эта функция потерь заставляет студента предсказывать именно "правильный" токен.

КомбинированиеL_{soft} иL_{hard}:

* Комбинирование "мягких" и "жестких" потерь позволяет студенту учиться как у учителя (черезL_{soft}), так и из исходных данных (черезL_{hard}).

* Коэффициент\alpha позволяет настроить баланс.

* Высокое\alpha (например, 0.9) означает, что мы больше полагаемся на знания учителя, переданные через "мягкие" метки. Это может быть полезно, когда учитель обладает значительно лучшими знаниями, чем можно извлечь только из "жестких" меток.

* Низкое\alpha (например, 0.5) означает, что мы в равной степени учитываем как знания учителя, так и "жесткие" метки. Это может быть полезно, когда мы хотим, чтобы студент сохранил способность хорошо работать и на исходных данных, а не только имитировал учителя.

Практическая реализация Soft-label Distillation для GPT моделей

Программный код был заимствован из репозитория: https://github.com/arcee-ai/DistillKit

1. Конфигурация дистилляции

Первым шагом необходимо настроить параметры дистилляции, включая температуру и коэффициент баланса между мягкими и жесткими метками:

"""
Здесь temperature: 2.0 соответствует параметру T в формулах, который "смягчает" распределение вероятностей, а alpha: 0.5 - это коэффициент α, который определяет соотношение между потерями от мягких и жестких меток.
"""

config = {
    "project_name": "distil-multilayer",    # Название проекта
    "dataset": {
        "name": "mlabonne/FineTome-100k",   # Название датасета
        "split": "train",                   # Раздел датасета для тренировки
        "num_samples": 1000,                # Количество образцов для тренировки (можно ограничить)
        "seed": 42                          # Значение для инициализации генератора случайных чисел
    },
    "models": {
        "teacher": "arcee-ai/Arcee-Spark",  # Модель учителя
        "student": "Qwen/Qwen2-1.5B"        # Модель студента
    },
    "tokenizer": {
        "max_length": 4096,                 # Максимальная длина токенов
        "chat_template": (
            "{% for message in messages %}"
            "{% if loop.first and messages[0]['role'] != 'system' %}"
            "{{ '<|im_start|>system\nYou are a helpful assistant.<|im_end|>\n' }}"
            "{% endif %}"
            "{{'<|im_start|>' + message['role'] + '\n' + message['content'] + '<|im_end|>' + '\n'}}"
            "{% endfor %}"
            "{% if add_generation_prompt %}"
            "{{ '<|im_start|>assistant\n' }}"
            "{% endif %}"
        )                                    # Шаблон для форматирования сообщений в чате
    },
    "training": {
        "output_dir": "./results",           # Директория для сохранения результатов
        "num_train_epochs": 3,               # Количество эпох для тренировки
        "per_device_train_batch_size": 1,    # Размер батча для тренировки на одном устройстве
        "gradient_accumulation_steps": 8,    # Количество шагов для накопления градиентов
        "save_steps": 1000,                  # Шаги для сохранения модели
        "logging_steps": 2,                  # Шаги для логирования
        "save_total_limit": 2,               # Лимит на количество сохраняемых моделей
        "learning_rate": 2e-5,               # Скорость обучения
        "weight_decay": 0.01,                # Коэффициент регуляризации
        "warmup_ratio": 0.2,                 # Доля шагов для разгона скорости обучения
        "lr_scheduler_type": "linear",       # Тип планировщика скорости обучения
        "resume_from_checkpoint": None,      # Путь к чекпоинту для возобновления тренировки (если есть)
        "fp16": False,                       # Использовать ли 16-битное число с плавающей точкой
        "bf16": True,                        # Использовать ли BFloat16
        "max_grad_norm": 1.0,                # Максимальная норма градиента
        "group_by_length": False             # Группировать ли батчи по длине
    },
    "distillation": {
        "temperature": 2.0,                  # Температура для дистилляции
        "alpha": 0.5                         # Коэффициент альфа для дистилляции
    },
    "model_config": {
        "use_flash_attention": True          # Использовать ли Flash Attention
    }
}

2. Подготовка моделей учителя и студента

Для дистилляции необходимо загрузить как модель-учитель (более крупную), так и модель-студент (более компактную):

import torch
from typing import Dict, Any
from transformers import AutoModelForCausalLM

def load_models_with_flash_attention(config: Dict[str, Any]) -> Dict[str, AutoModelForCausalLM]:
    """
    Description:
    ---------------
        Загружает модели с настройкой флеш-внимания для ускорения.

    Args:
    ---------------
        config: Конфигурация моделей и параметров

    Returns:
    ---------------
        Словарь с загруженными моделями

    Raises:
    ---------------
        KeyError: Если в конфигурации отсутствуют необходимые ключи

    Examples:
    ---------------
        >>> config = {
        ...     "model_config": {"use_flash_attention": True},
        ...     "models": {"teacher": "teacher_model_path", "student": "student_model_path"}
        ... }
        >>> load_models_with_flash_attention(config)
        {'teacher_model': <transformers.models.model_name.model.ModelName object>,
         'student_model': <transformers.models.model_name.model.ModelName object>}
    """
    # Настройки для загрузки моделей
    model_kwargs: Dict[str, Any] = {"torch_dtype": torch.bfloat16}

    # Проверка на использование flash attention
    if config["model_config"]["use_flash_attention"]:
        model_kwargs["attn_implementation"] = "flash_attention_2"

    # Загрузка моделей
    teacher_model = AutoModelForCausalLM.from_pretrained(config["models"]["teacher"], **model_kwargs)
    student_model = AutoModelForCausalLM.from_pretrained(config["models"]["student"], **model_kwargs)

    return {"teacher_model": teacher_model, "student_model": student_model}

# Вызов функции
models = load_models_with_flash_attention(config)

# Теперь models содержит загруженные модели
teacher_model = models["teacher_model"]
student_model = models["student_model"]

3. Реализация функции потерь с мягкими метками

Ключевым компонентом является функция потерь Soft-label Distillation. Рассмотрим её реализацию из файла distil_logits.py:

"""
Это прямая реализация формулы KL-дивергенции. Обратите внимание на следующие ключевые моменты:

1. Логиты масштабируются температурой T перед применением функций softmax/log_softmax.
2. Потери умножаются на T² для компенсации уменьшения градиентов, как описано в теории.
3. Финальная функция потерь комбинирует мягкие метки (KL-дивергенция) и жесткие метки (original_loss) с коэффициентом α.
"""

from typing import Any
import torch
import torch.nn.functional as F

def distillation_loss(
    self,
    student_logits: torch.Tensor,
    teacher_logits: torch.Tensor,
    inputs: Any,
    original_loss: torch.Tensor,
    config: Dict[str, Any]
) -> torch.Tensor:
    """
    Description:
    ---------------
        Вычисляет потери дистилляции между логитами студента и учителя.

    Args:
    ---------------
        student_logits: Логиты студента.
        teacher_logits: Логиты учителя.
        inputs: Входные данные.
        original_loss: Исходные потери.
        config: Конфигурация моделей и параметров.

    Returns:
    ---------------
        Общие потери, включающие дистилляционные потери и исходные потери.

    Raises:
    ---------------
        KeyError: Если в конфигурации отсутствуют необходимые ключи.

    Examples:
    ---------------
        >>> config = {
        ...     "distillation": {"temperature": 2.0, "alpha": 0.5},
        ...     "tokenizer": {"max_length": 512}
        ... }
        >>> student_logits = torch.randn(3, 512)
        >>> teacher_logits = torch.randn(3, 512)
        >>> inputs = ...
        >>> original_loss = torch.tensor(0.5)
        >>> distillation_loss(self, student_logits, teacher_logits, inputs, original_loss, config)
        tensor(0.25)
    """
    # Приведение размерностей логитов учителя и студента к одинаковому размеру
    student_logits, teacher_logits = pad_logits(
        student_logits.to(self.model.device),
        teacher_logits.to(self.model.device)
    )

    # Масштабирование логитов с помощью температуры T
    temperature = config["distillation"]["temperature"]
    student_logits_scaled = student_logits / temperature
    teacher_logits_scaled = teacher_logits / temperature

    # Расчёт KL-дивергенции между распределениями учителя и студента
    loss_kd = F.kl_div(
        F.log_softmax(student_logits_scaled, dim=-1),  # log(q_i^T)
        F.softmax(teacher_logits_scaled, dim=-1),      # p_i^T
        reduction='batchmean'
    ) * (temperature ** 2) / config["tokenizer"]["max_length"]

    # Комбинирование потерь от мягких и жестких меток
    alpha = config["distillation"]["alpha"]
    total_loss = alpha * loss_kd + (1 - alpha) * original_loss

    return total_loss

4. Обработка различных размеров словарей

Поскольку модели учителя и студента могут иметь разный размер словаря токенов, необходима дополнительная функция для согласования размерности их логитов:

"""
Эта функция добавляет нулевые логиты к меньшему распределению, чтобы обеспечить одинаковую размерность для сравнения распределений.
"""

from typing import Tuple
import torch

def pad_logits(
    student_logits: torch.Tensor,
    teacher_logits: torch.Tensor
) -> Tuple[torch.Tensor, torch.Tensor]:
    """
    Description:
    ---------------
        Приводит размерности логитов студента и учителя к одинаковому размеру.

    Args:
    ---------------
        student_logits: Логиты студента.
        teacher_logits: Логиты учителя.

    Returns:
    ---------------
        Кортеж из логитов студента и учителя с одинаковыми размерностями.

    Raises:
    ---------------
        ValueError: Если размерности логитов не совпадают и не могут быть приведены к одинаковому размеру.

    Examples:
    ---------------
        >>> student_logits = torch.randn(3, 512)
        >>> teacher_logits = torch.randn(3, 510)
        >>> pad_logits(student_logits, teacher_logits)
        (tensor([...]), tensor([...]))
    """
    # Определение размеров логитов
    student_size, teacher_size = student_logits.size(-1), teacher_logits.size(-1)

    # Если размеры не совпадают, добавляем паддинг
    if student_size != teacher_size:
        pad_size = abs(student_size - teacher_size)
        pad_tensor = torch.zeros(
            (*teacher_logits.shape[:-1], pad_size),
            dtype=teacher_logits.dtype,
            device=teacher_logits.device
        )

        # Возвращаем логиты с добавленным паддингом
        if student_size < teacher_size:
            return torch.cat([student_logits, pad_tensor], dim=-1), teacher_logits
        else:
            return student_logits, torch.cat([teacher_logits, pad_tensor], dim=-1)

    # Возвращаем логиты без изменений, если размеры совпадают
    return student_logits, teacher_logits

5. Кастомный тренер для дистилляции

Для интеграции процесса дистилляции в процесс обучения создаётся специальный класс тренера, который переопределяет функцию вычисления потерь:

"""
Этот класс:
1. Получает выходы (логиты) как от студента, так и от учителя
2. Замораживает веса учителя с помощью `torch.no_grad()`
3. Вычисляет комбинированную функцию потерь с использованием потерь от мягких и жестких меток
"""

from typing import Dict, Any, Union, Tuple
import torch
import torch.nn.functional as F
from transformers import SFTTrainer

class LogitsTrainer(SFTTrainer):
    """
    Description:
    ---------------
        Класс для обучения модели с использованием дистилляции логитов.
    """

    def compute_loss(
        self,
        model: torch.nn.Module,
        inputs: Dict[str, Any],
        return_outputs: bool = False
    ) -> Union[torch.Tensor, Tuple[torch.Tensor, Any]]:
        """
        Description:
        ---------------
            Вычисляет комбинированную функцию потерь для модели студента и учителя.

        Args:
        ---------------
            model: Модель студента.
            inputs: Входные данные.
            return_outputs: Флаг для возврата выходов модели.

        Returns:
        ---------------
            Комбинированная функция потерь и, если указано, выходы модели.

        Raises:
        ---------------
            ValueError: Если входные данные не соответствуют ожидаемым.

        Examples:
        ---------------
            >>> model = ...
            >>> inputs = ...
            >>> trainer = LogitsTrainer()
            >>> trainer.compute_loss(model, inputs, return_outputs=True)
            (tensor(0.5), ...)
        """
        # Перемещение входных данных на устройство модели
        inputs = {k: v.to(model.device) if hasattr(v, 'to') else v for k, v in inputs.items()}

        # Перемещение модели учителя на устройство модели
        self.teacher_model = self.teacher_model.to(model.device)

        # Получение модулей моделей, если они существуют
        student_model = model.module if hasattr(model, 'module') else model
        teacher_model = self.teacher_model.module if hasattr(self.teacher_model, 'module') else self.teacher_model

        # Получение выходов моделей
        student_outputs = student_model(**inputs)
        with torch.no_grad():  # Учитель не обучается
            teacher_outputs = teacher_model(**inputs)

        # Вычисление комбинированной функции потерь
        custom_loss = self.distillation_loss(
            student_outputs.logits,
            teacher_outputs.logits,
            inputs,
            student_outputs.loss
        )

        # Возврат потерь и выходов модели, если указано
        if return_outputs:
            return custom_loss, student_outputs
        return custom_loss

    def pad_logits(
        self,
        student_logits: torch.Tensor,
        teacher_logits: torch.Tensor
    ) -> Tuple[torch.Tensor, torch.Tensor]:
        """
        Description:
        ---------------
            Приводит размерности логитов студента и учителя к одинаковому размеру.

        Args:
        ---------------
            student_logits: Логиты студента.
            teacher_logits: Логиты учителя.

        Returns:
        ---------------
            Кортеж из логитов студента и учителя с одинаковыми размерностями.

        Raises:
        ---------------
            ValueError: Если размерности логитов не совпадают и не могут быть приведены к одинаковому размеру.

        Examples:
        ---------------
            >>> student_logits = torch.randn(3, 512)
            >>> teacher_logits = torch.randn(3, 510)
            >>> trainer = LogitsTrainer()
            >>> trainer.pad_logits(student_logits, teacher_logits)
            (tensor([...]), tensor([...]))
        """
        # Определение размеров логитов
        student_size, teacher_size = student_logits.size(-1), teacher_logits.size(-1)

        # Если размеры не совпадают, добавляем паддинг
        if student_size != teacher_size:
            pad_size = abs(student_size - teacher_size)
            pad_tensor = torch.zeros(
                (*teacher_logits.shape[:-1], pad_size),
                dtype=teacher_logits.dtype,
                device=teacher_logits.device
            )

            # Возвращаем логиты с добавленным паддингом
            if student_size < teacher_size:
                return torch.cat([student_logits, pad_tensor], dim=-1), teacher_logits
            else:
                return student_logits, torch.cat([teacher_logits, pad_tensor], dim=-1)

        # Возвращаем логиты без изменений, если размеры совпадают
        return student_logits, teacher_logits

    def distillation_loss(
        self,
        student_logits: torch.Tensor,
        teacher_logits: torch.Tensor,
        inputs: Any,
        original_loss: torch.Tensor
    ) -> torch.Tensor:
        """
        Description:
        ---------------
            Вычисляет потери дистилляции между логитами студента и учителя.

        Args:
        ---------------
            student_logits: Логиты студента.
            teacher_logits: Логиты учителя.
            inputs: Входные данные.
            original_loss: Исходные потери.

        Returns:
        ---------------
            Общие потери, включающие дистилляционные потери и исходные потери.

        Raises:
        ---------------
            KeyError: Если в конфигурации отсутствуют необходимые ключи.

        Examples:
        ---------------
            >>> config = {
            ...     "distillation": {"temperature": 2.0, "alpha": 0.5},
            ...     "tokenizer": {"max_length": 512}
            ... }
            >>> student_logits = torch.randn(3, 512)
            >>> teacher_logits = torch.randn(3, 512)
            >>> inputs = ...
            >>> original_loss = torch.tensor(0.5)
            >>> trainer = LogitsTrainer()
            >>> trainer.distillation_loss(student_logits, teacher_logits, inputs, original_loss)
            tensor(0.25)
        """
        # Приведение размерностей логитов учителя и студента к одинаковому размеру
        student_logits, teacher_logits = self.pad_logits(
            student_logits.to(self.model.device),
            teacher_logits.to(self.model.device)
        )

        # Масштабирование логитов с помощью температуры T
        temperature = config["distillation"]["temperature"]
        student_logits_scaled = student_logits / temperature
        teacher_logits_scaled = teacher_logits / temperature

        # Расчёт KL-дивергенции между распределениями учителя и студента
        loss_kd = F.kl_div(
            F.log_softmax(student_logits_scaled, dim=-1),  # log(q_i^T)
            F.softmax(teacher_logits_scaled, dim=-1),      # p_i^T
            reduction='batchmean'
        ) * (temperature ** 2) / config["tokenizer"]["max_length"]

        # Комбинирование потерь от мягких и жестких меток
        alpha = config["distillation"]["alpha"]
        total_loss = alpha * loss_kd + (1 - alpha) * original_loss

        return total_loss

6. Подготовка тренера и запуск обучения

После определения всех компонентов можно инициализировать тренер и запустить процесс дистилляции:

"""
Обратите внимание, что модель-учитель добавляется к тренеру как атрибут, чтобы она была доступна внутри функции `compute_loss`.
"""

# Импорт необходимых библиотек
from transformers import TrainingArguments
from accelerate import Accelerator

# Инициализация accelerator
accelerator = Accelerator()

# Аргументы обучения
training_arguments = TrainingArguments(**config["training"])

# Проверка наличия предобработанного датасета
if 'tokenized_dataset' not in locals():
    # Если датасет не предобработан, выполняем необходимую предобработку
    # Код предобработки датасета должен быть здесь...
    print("Необходимо сначала выполнить предобработку датасета!")

# Создание кастомного SFT тренера
trainer = LogitsTrainer(
    model=student_model,
    train_dataset=tokenized_dataset["train"],
    eval_dataset=tokenized_dataset["test"],
    tokenizer=student_tokenizer,
    args=training_arguments,
    max_seq_length=config["tokenizer"]["max_length"],
    dataset_text_field="text",
)

# Добавление модели-учителя к тренеру
trainer.teacher_model = teacher_model

# Подготовка к распределенному обучению
trainer = accelerator.prepare(trainer)

# Запуск обучения
trainer.train(resume_from_checkpoint=config["training"]["resume_from_checkpoint"])

# Сохранение финальной модели
trainer.save_model(config["training"]["output_dir"])

print(f"Обучение завершено. Модель сохранена в {config['training']['output_dir']}")

Преимущества Soft-label Distillation:

  • Более полная передача знаний: Студент получает доступ к "темным знаниям" учителя — информации о сложных случаях, тонких различиях между классами и степени неопределенности.

  • Лучшие результаты: Студенты, обученные этим методом, обычно демонстрируют производительность ближе к учителю по сравнению с Hard-label Distillation.

  • Улучшенная генерализация: Модели лучше работают на новых данных, так как учатся не только "что" предсказывать, но и "с какой уверенностью".

  • Контроль через температуру: Параметр T позволяет настраивать степень "мягкости" дистилляции. Более высокие значения T делают распределение более равномерным, помогая передать больше информации о маловероятных классах.

  • Совместимость с другими методами: Легко комбинируется с другими техниками улучшения моделей.

Недостатки Soft-label Distillation:

  • Вычислительные затраты: Для языковых моделей с большими словарями (50,000+ токенов) хранение и передача полных распределений вероятностей требует значительных ресурсов.

  • Сложность реализации: Требует доступа к логитам/вероятностям учителя, а не только к финальным предсказаниям.

  • Настройка гиперпараметров: Необходимо тщательно подбирать температуру T и коэффициент α для оптимальных результатов.

  • Зависимость от качества учителя: Если учитель имеет систематические ошибки, они могут передаться студенту.

Сравнение Hard-label и Soft-label Distillation:

Аспект

Hard-label Distillation

Soft-label Distillation

Передаваемая информация

Только итоговые классы/токены

Полные распределения вероятностей

Температура

Не используется

Используется для "смягчения" распределений

Сложность реализации

Простая

Средняя

Вычислительные требования

Низкие

Средние-высокие

Объем хранимых данных

Малый

Большой (особенно для языковых моделей)

Качество получаемой модели

Хорошее

Лучшее

Способность передавать неопределенность

Низкая

Высокая

Эффективность для языковых моделей

Средняя

Высокая

В заключение, Soft-label Distillation предлагает более мощный метод передачи знаний от учителя к ученику, особенно для сложных задач, где важны тонкие различия между классами и понимание неопределенности. Ключевое отличие от Hard-label Distillation заключается в использовании полных распределений вероятностей и temperature scaling, что позволяет извлечь "темные знания" и научить студента не только выдавать правильные ответы, но и воспроизводить тонкие нюансы рассуждений учителя.

Part 2: Законы масштабирования дистилляции

После того, как DeepSeek представил в open source свой метод дистилляции знаний для R1, исследователи из Apple и Оксфордского университета быстро предложили закон масштабирования дистилляции и уже 28 февраля завершили все эксперименты и загрузили 67-страничную статью на arXiv.

Рассмотрим мотивацию исследования, которая сводится к следующим пунктам:

  1. Текущее состояние исследований законов масштабирования моделей: В последние годы исследования выявили взаимосвязь между производительностью языковых моделей, их размером и объемом данных для обучения. Однако систематических исследований законов масштабирования в контексте дистилляции пока не проводилось.

  2. Проблема стоимости вывода модели: С увеличением размера языковых моделей значительно возрастает стоимость вывода. Исследование того, как снизить стоимость вывода без потери производительности, становится важной задачей.

  3. Эффективность и производительность дистилляции: Теоретически, дистилляция может снизить стоимость вывода, однако в академических кругах нет единого мнения относительно методов дистилляции, особенно в том, как рационально распределить вычислительные ресурсы для создания наиболее мощных моделей, что остается большой неопределенностью.

Экстраполяция закона масштабирования дистилляции
Экстраполяция закона масштабирования дистилляции

Экстраполяции закона масштабирования дистилляции. Закон масштабирования дистилляции (Уравнение 8) аппроксимирован на слабых учениках L_S > 2.3 для ряда учителей с потерямиL_T. Сплошные линии представляют прогнозируемое поведение модели для невидимых учителей при заданной конфигурации ученика (интерполяция), а пунктирные линии представляют прогнозируемое поведение модели за пределами видимых учителей и для области сильных учеников ( L_S \leq 2.3 ).

Закон масштабирования дистилляции

Традиционный закон масштабирования (Scaling Laws) для больших моделей демонстрирует, что производительность языковой модели (LM) может улучшаться с увеличением вычислительных ресурсов, если модель следует оптимальной вычислительной парадигме обучения. Однако постоянный рост затрат на инференс делает этот подход все менее практичным, что заставляет исследователей искать альтернативные методы, включая переобучение и дистилляцию, для создания небольших, но мощных моделей.

Исследователи провели обширные эксперименты, используя модели-студенты и модели-учителя с параметрами от 143 миллионов до 12,6 миллиардов и объемом данных до 512 миллиардов токенов. Целью было изучить взаимосвязь между производительностью модели и вычислительными ресурсами в процессе дистилляции, а также найти способы оптимизации распределения этих ресурсов.

В следующей таблице показано значение символов, используемых в этой статье:

Таблица. Выражения, связанные с законами масштабирования, используемые в данной работе. В каждом случаеS всегда относится к ученику, а не к обучению с учителем.

Выражение

Значение

N / N_S / N_T

Количество параметров модели/ученика/учителя, не связанных с эмбеддингом. В тексте, когда мы упоминаем параметры, мы всегда имеем в виду параметры, не связанные с эмбеддингом, если не указано иное. Подробности см. в Приложении H.2.

D / D_T

Количество токенов, на которых предобучена модель/учитель.

D_S

Количество токенов, на которых дистиллирован ученик.

M \equiv D / N

Соотношение токенов на параметр, или MM-соотношение. В работе Hoffmann et al. (2022), M принимает оптимальное значение M^∗≈20, что является эмпирическим правилом Chinchilla.

L \approx L(N, D)

Кросс-энтропия модели, которая представляет собой валидационную кросс-энтропию модели на данных, оцениваемую по закону масштабирования с учителем для модели с N параметрами, обученной на D токенах. (Уравнение 1).

L_T \approx L(N_T, D_T)

Кросс-энтропия учителя, которая представляет собой валидационную кросс-энтропию учителя на данных, оцениваемую по закону масштабирования с учителем для учителя с N_T​ параметрами, обученного на D_T​ токенах.

L_S \approx L_S(N_S, D_S, L_T)

Кросс-энтропия ученика, которая представляет собой валидационную кросс-энтропию ученика на данных, оцениваемую по нашему закону масштабирования дистилляции для ученика с N_S​ параметрами, дистиллированного на D_S​ токенах с использованием учителя с потерей предобучения L_T​ (Уравнение 8).

\tilde{L}_S \approx L(N_S, D_S)

Кросс-энтропия ученика с учителем, которая представляет собой валидационную кросс-энтропию ученика на данных, если бы ученик был обучен с учителем, оцениваемую по закону масштабирования с учителем для ученика с N_S​ параметрами, обученного наD_S​ токенах.

Пояснение: Кросс-энтропия — это метрика, измеряющая расхождение между предсказанным распределением вероятностей модели и истинным распределением. Чем ниже кросс-энтропия, тем лучше модель предсказывает правильные токены. Это основной показатель качества языковой модели.

Пояснение к правилу Чинчиллы: Исследование Hoffmann et al. (2022) установило эмпирическое правило оптимального соотношения между количеством параметров модели и количеством токенов для обучения — примерно 20 токенов на каждый параметр. Это правило позволяет эффективно распределять вычислительные ресурсы при обучении крупных языковых моделей.

Формализация закона масштабирования дистилляции

Центральным вкладом исследования является формулировка закона масштабирования дистилляции:

L_S(N_S, D_S, L_T) = L_T + \frac{1}{L_{c_0}^T} \left( 1 + \left( \frac{L_T}{\tilde{L}_S^{d_1}} \right)^{1/f_1} \right)^{-c_1f_1} \left( \frac{A}{N_S^{\alpha'}} + \frac{B}{D_S^{\beta'}} \right)^{\gamma'}

Объяснение переменных:

L_S(N_S, D_S, L_T) — кросс-энтропия студента (мера ошибки предсказания; чем ниже, тем лучше модель).

L_T — кросс-энтропия учителя (мера ошибки предсказания большой модели).

N_S — количество неэмбеддинговых параметров студента (основные обучаемые параметры модели).

D_S — количество токенов, использованных для обучения студента при дистилляции.

\tilde{L}_S = L(N_S, D_S) — потенциальная кросс-энтропия студента при обычном обучении без дистилляции, определяемая классическим законом масштабирования:

L(N, D) = E - \frac{A}{N^\alpha} - \frac{B}{D^\beta}

\{c_0, c_1, d_1, f_1, \alpha', \beta', \gamma'\} — коэффициенты, определяемые эмпирически.

A иB — положительные коэффициенты, зависящие от архитектуры модели и характеристик набора данных.

Физический смысл формулы:

1. Базовая часть:L_T — студент не может быть лучше учителя.

2. Модифицирующая часть: Остальная часть формулы описывает, насколько эффективно студент может приблизиться к учителю в зависимости от своего размера, количества данных и качества учителя.

Ключевые выводы:

1. Студент не может превзойти учителя (всегдаL_S \geq L_T). Кросс-энтропия (L) - это мера ошибки модели. Чем ниже значение L, тем лучше модель предсказывает данные.

2. Чем ближе потенциальная производительность студента к производительности учителя, тем эффективнее дистилляция.

3. При фиксированном учителе закон масштабирования дистилляции не превосходит обычный закон масштабирования.

Практическое применение:

Этот закон позволяет оптимально распределить вычислительные ресурсы между учителем и студентом и прогнозировать эффективность дистилляции.

То есть: Этот закон описывает, как качество маленькой модели зависит от трех факторов: размера самой модели, количества данных для обучения и качества большой модели-учителя. Ключевой вывод: студент никогда не может быть лучше учителя, но насколько близко он подойдет к учителю, зависит от его собственных возможностей и объема тренировки.

Коэффициенты смешивания в процессе дистилляции знаний

Рассмотрев общий закон масштабирования дистилляции, важно также понять практические аспекты реализации этого процесса, в частности, как управлять балансом между имитацией учителя и самостоятельным обучением модели-ученика.

Основная идея дистилляции знаний заключается в переносе информации от большой модели-учителя к компактной модели-ученику. В этом процессе прогнозируемое распределение вероятностей модели-учителя используется в качестве целевого распределения для модели-ученика. Обучение происходит путем минимизации расхождения Кульбака-Лейблера (KL-дивергенции) между распределениями ученика и учителя:

{L}_{\text{KD}} \left( z_T^{(i)}, z_S^{(i)} \right) = -\tau^2 \sum_{a=1}^V \sigma_a \left( \frac{z_T^{(i)}}{\tau} \right) \log \sigma_a \left( \frac{z_S^{(i)}}{\tau} \right)

где:

-z_T^{(i)} иz_S^{(i)} — выходные логиты моделей учителя и ученика соответственно

-\tau — температура дистилляции, контролирующая "сглаженность" распределения вероятностей учителя

-\sigma_a — функция softmax, преобразующая логиты в вероятности

-V — размер словаря

Комбинированная функция потерь для модели-ученика объединяет несколько компонентов:

{L}_S\big(x^{(i)}, \boldsymbol{z}_T^{(i)},\boldsymbol{z}_S^{(i)}\big) = (1-\lambda)\,{L}_{\textrm{NTP}}(x^{(i)},\boldsymbol{z}_S^{(i)}) + \lambda\,{L}_{\textrm{KD}}(\boldsymbol{z}_T^{(i)},\boldsymbol{z}_S^{(i)}) + \lambda_Z\,{L}_Z(\boldsymbol{z}_S^{(i)})

где:

-{L}_{\textrm{NTP}} — потеря при предсказании следующего токена (стандартная кросс-энтропия)

-{L}_{\textrm{KD}}— потеря при дистилляции знаний (KL-дивергенция)

-{L}_Z— регуляризационная Z-потеря, стабилизирующая обучение путем нормализации логитов

-\lambda— коэффициент смешивания, определяющий баланс между обучением на "чистых" данных и имитацией учителя

-\lambda_Z— весовой коэффициент для Z-потери

Экспериментальное определение оптимальных параметров дистилляции

Для определения влияния параметров дистилляции на эффективность закона масштабирования, исследователи провели серию экспериментов. Чтобы исключить влияние данных и сосредоточиться именно на роли модели-учителя, эксперименты проводились в режиме "чистой дистилляции" с λ=1. Результаты показали, что такой выбор λ даёт результаты, статистически сопоставимые с использованием оптимальных значений λ^∗.

Во всех экспериментах использовалась фиксированная температура дистилляции τ=1, которая эмпирически показала наилучшую эффективность для обучения модели-ученика.

Коэффициенты смешивания λ
Коэффициенты смешивания λ

Коэффициенты смешивания\lambda.

(a) Модели-ученики шести размеровN_S \in \{198M, 266M, \ldots, 2.72B\}, обученные с соотношением M = D_S/N_S = 20, дистиллируются от моделей-учителей размеров N_T \in \{546M, 975M, \ldots, 7.75B\}, обученных с соотношениеM = D_T/N_T = 20, с различными значениями коэффициента смешивания \lambda \in [0, 1]. Значения\lambda = 0 и\lambda = 1 соответствуют стандартному обучению и чистой дистилляции соответственно.

(b) Оптимальные коэффициенты смешивания\lambda^* = \arg \min_{\lambda} {L}(\lambda), дающие наименьшую потерю на валидационном наборе для каждой пары учитель-ученик.

Эти эксперименты подтверждают, что параметры дистилляции оказывают существенное влияние на итоговую производительность модели-ученика, и их оптимальный выбор напрямую связан с размерами моделей учителя и ученика, что согласуется с общим законом масштабирования дистилляции.

Вывод

Дистилляция знаний — это метод, позволяющий передать способности большой нейронной модели (учителя) меньшей и вычислительно эффективной модели (ученику). Процесс основан на обучении модели-ученика имитировать распределение вероятностей модели-учителя путём минимизации расхождения Кульбака-Лейблера между их предсказаниями.

Эффективность дистилляции определяется балансом нескольких компонентов в функции потерь:

  • Стандартной кросс-энтропии при предсказании следующего токена

  • KL-дивергенции при имитации учителя

  • Регуляризационной Z-потери для стабилизации обучения

Два ключевых параметра контролируют этот процесс:

  • Коэффициент смешивания λ, регулирующий баланс между самостоятельным обучением и имитацией учителя

  • Температура дистилляции τ, влияющая на "сглаженность" распределения вероятностей

Экспериментальные исследования демонстрируют, что режим "чистой дистилляции" (λ = 1) при температуре τ = 1 часто даёт результаты, сопоставимые с оптимально подобранными параметрами. Однако наиболее важным открытием является то, что идеальные значения этих параметров системно зависят от соотношения размеров конкретной пары моделей учитель-ученик.

Это открытие соответствует общему закону масштабирования дистилляции и имеет прямое практическое применение: для достижения максимальной эффективности при практической реализации дистилляции необходим индивидуальный подбор параметров с учётом размеров используемых моделей, что позволяет существенно улучшить итоговую производительность компактной модели при сохранении её вычислительной эффективности.

Эксперимент с фиксированным учитилем и разными учениками

Размер модели учителя и объем обучающих данных на которых обучался учитель, фиксированы, а размер модели ученика и объем дистилляционных данных варьируются. Цель состоит в том, чтобы изучить, как производительность модели ученика меняется в зависимости от ее размера и объема обработанных дистилляционных данных в условиях фиксированной модели учителя. Таким образом, можно определить оптимальную производительность модели студента при различных масштабах и объемах данных.

Figure_5
Figure_5
Figure_6
Figure_6

Из результатов эксперимента можно заметить, что:

  • При высокой вычислительной мощности, чем больше масштаб параметров модели ученика, тем меньше его функция потерь, и чем больше масштаб модели учителя, тем очевиднее эта тенденция.

  • Когда размер моделей ученика и учителя определен, становится понятно, что чем больше вычислительная мощность, тем лучше будет работать модель ученика.

  • При низкой вычислительной мощности производительность модели сначала улучшится, а затем ослабнет с размером модели. Здесь легко понять, что более крупные модели не полностью обучаются при меньшей вычислительной мощности.

  • В особых случаях модель ученика может превзойти модель учителя и показать способность к обобщению. Я лично предполагаю, что модель учителя может быть недообучена в таких сценариях.

Эксперимент с фиксированным учеником и разными учителями

Размер модели ученика и объем данных дистилляции фиксированы, а размер модели учителя и объем обучающих данных варьируются. Цель состоит в том, чтобы изучить, как эффективность модели учителя влияет на конечную эффективность модели ученика. Таким образом, можно определить оптимальный размер модели учителя и объем обучающих данных для максимизации производительности модели ученика.

Figure_7
Figure_7

Как видно из результатов, чем больше параметры у модели учителя, тем ниже перекрестная энтропия модели ученика. Это показывает, что для достижения наилучшего эффекта дистилляции производительность модели учителя должна соответствовать возможностям модели ученика.

Дистилляция против контролируемого обучения

Чтобы понять, когда дистилляция приносит пользу, на следующем рисунке сравнивается производительность дистилляции и контролируемого обучения при фиксированных вычислительных ресурсах. Результаты показывают, что контролируемое обучение всегда превосходит дистилляцию при наличии достаточного количества вычислений или данных у учащихся. При умеренном бюджете данных дистилляция имеет преимущества, однако при наличии больших объемов данных контролируемое обучение превосходит дистилляцию.

Подводя итог, можно сказать, что при ограниченных вычислительных ресурсах дистилляция обычно более эффективна, чем контролируемое обучение. Это связано с тем, что дистилляция может быстрее усваивать эффективные представления признаков под руководством модели учителя, тем самым достигая более высокой производительности при меньших вычислительных ресурсах.

Figure_8
Figure_8

Выбор модели учителя

  • Сила обучающего сигнала: Модели учителей разных размеров могут обеспечивать разную силу обучающего сигнала, которая обычно измеряется с помощью потери перекрестной энтропии. Более крупная модель учителя может обеспечить более сильный сигнал обучения (более низкая перекрестная энтропия), тем самым помогая модели ученика лучше учиться.

  • Увеличение затрат: использование более крупной модели учителя повлечет за собой более высокие затраты из-за необходимости вычисления логитов модели учителя. Это означает, что более крупная модель учителя не только более затратна в обучении, но и потребляет больше вычислительных ресурсов при использовании для дистилляции.

На рисунке ниже показано изменение потери перекрестной энтропии модели студента при различных бюджетах данных дистилляции. Результаты показывают, что оптимальная потеря учителя (представленная красной линией) уменьшается по степенному закону с увеличением численности учащихся до тех пор, пока потеря ученика не сравняется с оптимальной потерей учителя.

Figure_9
Figure_9

Как видно на другом рисунке ниже, по мере увеличения объема данных дистилляции, перекрестная энтропия оптимальной модели учителя постепенно уменьшается. Таким образом, можно сделать вывод, что: когда вычислительные ресурсы ограничены, выбор меньшей модели учителя может снизить затраты на вывод, при этом обеспечивая эффективные сигналы обучения для модели ученика.

Figure_10
Figure_10

Рассчитайте оптимальную дистилляцию

Целью вычислительно оптимальной дистилляции является определение способа создания модели студента желаемого размера с наименьшей перекрестной энтропией при заданном вычислительном бюджете. В частности, необходимо найти оптимальный объем данных для обучения учащихся, размер модели учителя, данные для обучения, чтобы минимизировать перекрестную энтропию студента и при этом удовлетворить ограничениям вычислительного бюджета.

На рисунке ниже мы видим:

  • Контролируемое обучение всегда соответствует наилучшему варианту настройки дистилляции при достаточном вычислительном бюджете: Контролируемое обучение всегда соответствует наилучшему варианту настройки дистилляции при определенном общем вычислительном бюджете. Это означает, что контролируемое обучение может достичь той же производительности, что и дистилляция, если вычислительный бюджет достаточно велик.

  • Если в вычисления включено обучение учителя, перекрестная энтропия учащихся всегда выше, чем в контролируемой обстановке: это означает, что если вашей единственной целью является создание наилучшей модели с целевым размером и у вас нет доступа к учителю, вам следует выбрать контролируемое обучение вместо обучения учителя и последующей дистилляции. Напротив, если цель состоит в том, чтобы выделить семейство моделей или использовать учителя в качестве обслуживающей модели, то выделение может оказаться более выгодным с вычислительной точки зрения, чем контролируемое обучение.

  • Меньшие модели с большей вероятностью получат выгоду от контролируемого предварительного обучения, в то время как более крупные модели с большей вероятностью получат выгоду от дистилляции: Меньшие модели с большей вероятностью получат выгоду от контролируемого обучения при больших вычислительных бюджетах, в то время как более крупные модели с большей вероятностью получат выгоду от дистилляции при больших вычислительных бюджетах.

Figure_11
Figure_11

На рисунке ниже показаны тенденции изменения оптимального размера учителя и объема обучающих данных по мере изменения вычислительного бюджета. Токены моделей студентов и преподавателей масштабируются по степенному закону, причем токены студентов растут быстрее. Размер лучшей модели учителя сначала увеличивается, пока не станет немного больше ученика, а затем стабилизируется. Это связано с тем, что использование большой модели учителя для вывода обходится дорого, и по мере увеличения количества токенов учеников более эффективным становится переобучение модели учителя.

Figure_12
Figure_12

Ключевые результаты исследования

В результате исследований авторы пришли к следующим выводам:

  1. Предсказуемость производительности через закон масштабирования: Производительность модели-студента размером N_S​, полученной путем дистилляции из модели-учителя размером N_T​ с использованием D_S​ токенов, может быть предсказана с помощью разработанного закона масштабирования дистилляции.

    Практическое значение: Это позволяет заранее оценить, какой результат можно получить от процесса дистилляции, не проводя дорогостоящих экспериментов. Компания может спланировать свои ресурсы и решить, стоит ли вкладываться в дистилляцию, или лучше выбрать другой подход к созданию эффективной модели.

  2. Влияние параметров учителя на студента: Размер модели-учителя NTNT​ и количество токенов для её обучения D_T​ определяют кросс-энтропию модели-учителя L_T=L_T(N_T,D_T), которая, в свою очередь, влияет на кросс-энтропию модели-студента.

    Наглядный пример: Представьте учителя как источник знаний для студента. Если учитель сам недостаточно образован (высокая кросс-энтропия), он не сможет хорошо обучить студента, какими бы способностями студент ни обладал.

  3. Феномен "разрыва в способностях": Исследование выявило интересный эффект - более сильный учитель может привести к худшему студенту, что объясняется "разрывом в способностях" (capacity gap). Влияние кросс-энтропии модели-учителя на потери модели-студента следует степенному закону, который переключается между двумя режимами в зависимости от относительной способности к обучению студента и учителя. Исследование показало, что важен именно разрыв в способности к обучению (гипотезное пространство и оптимизационная способность) между учителем и студентом, а не просто их относительный размер.

    Аналогия для понимания: Представьте, что профессор квантовой физики пытается обучить первоклассника. Несмотря на высокую квалификацию профессора, первоклассник не сможет усвоить сложный материал из-за разрыва в способностях к обучению. Аналогично, если модель-учитель слишком сложна и "мыслит" на уровне, недоступном модели-студенту, эффективность обучения снижается.

  4. U-образная зависимость ошибки студента: Эмпирически подтверждается U-образная зависимость ошибки студента от размера учителя при фиксированном размере студента, что теоретически обосновывается разрывом в емкости между ними.

    Визуальное представление: Если изобразить ошибку студента на графике, где по горизонтальной оси отложен размер учителя, мы увидим U-образную кривую. Это означает, что существует оптимальный размер учителя для данного студента — не слишком маленький (недостаточно знаний) и не слишком большой (слишком сложное представление знаний).

Практические рекомендации

Результаты исследования показывают, что дистилляция становится более эффективной, чем обучение с учителем, при соблюдении следующих условий:

  1. Общее количество вычислений или токенов для студента не превышает пороговое значение, связанное с размером студента, согласно новому закону масштабирования.

    Практический сценарий: Для компании с ограниченным бюджетом на вычисления, которая хочет создать модель размером 1 миллиард параметров, дистилляция может быть оптимальным выбором, если доступно менее 20 миллиардов токенов для обучения (согласно правилу Чинчиллы).

  2. Модель-учитель уже существует, или обучение модели-учителя имеет применение за пределами одной дистилляции.

    Бизнес-кейс: Если компания уже обучила крупную модель для своих основных задач, имеет смысл использовать её для дистилляции меньших, специализированных моделей для развертывания на мобильных устройствах или в средах с ограниченными ресурсами.

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    They froze my $275K in Bitcoin. Blockchain cyber retrieve took actions. Running a startup in Nigeria is already a wild ride power cuts, red tape, and FX rates that dance like Afrobeats. But the day the government banned crypto transactions? Game over. My funds were locked in an exchange wallet. No access, No help I tried everything VPNs, New accounts Support bots. Nothing changed, Then someone in a Signal group dropped the name: BLOCKCHAIN CYBER RETRIEVE. These folks didn’t fight the exchange they outsmarted it. Peer-to-peer protocols. DeFi tools. Secure escrow networks. Nine  days later, I got the email “Wallet restored. Check your balance. Every Single Satoshi. Was back. Since then? Fully decentralized, Unbothered, Unbanked. Whenever new laws try to stifle African innovation, I just sip palm wine and say: Let them try. We’ve got BLOCKCHAIN CYBER RETRIEVE now.” CONTACT THEM: Whatsapp +1, 5,2,0, 5,6,4, 8,3 0 0  Email: B L O C K C H A I N C Y B E R R E T R I E V E @ P O S T . C O M  OR   SUPPORT @ B L O C K C H A I N C Y B E R R E T R I E V E .O R G

  • 07.04.25 18:09 rashmiramesh

    I was introduced to crypto by my son a few years ago, I invested in USDT and BTC using Binance, I have several accounts including personal bank accounts so I was unable to keep up with all of them and ended up forgetting my secret codes used in accessing the account, I asked my son to help me since he had introduced me Crypto, unfortunately he gave me bad news that I had lost my investment, I was so heartbroken considering I had invested my life saving of $70,700, I narrated my ordeal to one of my friends who happened to know someone who had a similar experience, so after I met him he directed to where he got help, he told me that LEE ULTIMATE HACKER who were able to help him with his recovery problem, I quickly contacted them to help me with my lost funds, I was a bit skeptical about it coz of what I had gone through the last few days, the frustration and anxiety was getting to me, after contacting LEE ULTIMATE HACKER one of their team members took me through the recovery process explaining on how it works and what was required from my end ,he informed me that it would take 12 hours for my funds to be recovered, I was so anxious but they assured me that all will be well and soon enough I will be able to have full control of my wallet, true to their word LEE ULTIMATE HACKER team were able to recover my wallet and I was able to access and change my log ins to my wallet, I was so happy and I couldn’t believe it I logged in and out of my account a few times just to be sure, for any lost crypto contact LEE ULTIMATE HACKER via LEEULTIMATEHACKER @ AOL . COM telegram: LEEULTIMATE wh@tsapp +1 (715) 314 - 9248 the solution to all your recovery problems.

  • 07.04.25 18:32 elizabethrush89

    God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: Recovercapital AT cyberservices. com Contact Telegram: @Capitalcryptorecover

  • 07.04.25 18:32 elizabethrush89

    God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: Recovercapital AT cyberservices. com Contact Telegram: @Capitalcryptorecover

  • 07.04.25 21:03 elizabethrush89

    God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 08.04.25 03:00 natashaohnson

    Working in conflict zones means improvising. When normal banking channels failed us, our NGO relied on Bitcoin to buy medical supplies directly. It worked, until a missile strike took out our field office, along with the hardware wallet that stored $410,000 in funds. Overnight, our ability to deliver life-saving aid is paralyzed. Amidst the chaos, I reached out to contacts in the humanitarian world. A UN aid worker whispered a name: Cyber Constable Intelligence. "They're the ones who can help you recover lost crypto," he assured me. Despair and hope clashed as I dialed their team on a satellite phone in a conflict zone. What followed was nothing short of a virtual rescue mission. Cyber Constable Intelligence's blockchain forensic experts didn't simply "recover" our assets; they improvised a fix like battlefield medics performing triage. They tracked our wallet's blockchain timestamps, reconstructing lost credentials from synced backups and transaction history. Working under direst duress, we communicated information between spotty internet and backup power sources. Cyber Constable Intelligence team members improvised, rendering security protocols impenetrable as they worked through the jurisdictional nightmares of working within war zones. Every update from them was a pulse that kept our mission alive. After our last available backup failed, they instituted a complex cryptographic reconstruction technique, a process I still don't understand, but it worked. Twelve days later, my satellite device displayed a message: "Access restored. Funds secured." It was not money. It was bandages, antibiotics, clean water, and hope. Thanks to Cyber Constable Intelligence, we replenish our medical supplies, ensuring that patients, innocent victims who had been caught in the crossfire, received the treatment they deserved. More than restoration, they advised us on decentralized storage and multi-signature security for long-term durability. We don't simply utilize Bitcoin presently; we utilize it astutely. Now, each time I sign a crypto transaction, I remember that minute, receiving life-saving medication that might not have come but for this group. In times of war, not every hero wears a uniform. Some carry keyboards, hunting down lost assets and securing humanitarian aid. Cyber Constable Intelligence not only restored our crypto, they kept our mission in the battle. If you think Bitcoin is just an investment, think again. To us, it's a lifeline. CYBER CONSTABLE INTELLIGENCE INFO: WhatsApp: 1 252378-7611 Website info; www.cyberconstableintelligence.com Email Info [email protected] Telegram Info: https://t.me/cyberconstable

  • 10.04.25 23:26 patricialovick86

    How To Recover Your Bitcoin Without Falling Victim To Scams: A  Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 10.04.25 23:27 patricialovick86

    How To Recover Your Bitcoin Without Falling Victim To Scams: A  Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 11.04.25 00:48 patricialovick86

    How To Recover Your Bitcoin Without Falling Victim To Scams: A  Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 11.04.25 03:20 edwardoelliott6

    PROFESSIONAL MONEY RECOVERY AGENCY → FOLKWIN EXPERT RECOVERY. Hi, I’m sharing my ordeal today because I know many of you could be in the same situation, and I want to help you avoid the same mistake I made. A little over a month ago, I came across what seemed like an incredible deal for a movie streaming service. They promised all the latest movies, TV shows, and exclusive content for a very reasonable price. They were offering an annual subscription for just $39,000, which seemed like a great deal at the time when compared to some of the larger streaming services out there. I should’ve known something was off from the start. The website looked pretty legitimate, had professional graphics, and even customer reviews that were mostly positive. But there were no big, recognizable brand names behind it, and the service was claiming to have content from major studios, which raised a red flag I didn't fully process. Still, the deal was tempting, and after doing a quick search online (which, in hindsight, wasn’t thorough enough), I decided to go ahead and sign up. I paid the $39,000 upfront for the annual subscription, thinking that I was getting access to all the movies and shows I’d ever wanted. At first, everything seemed fine. I received an email confirming my subscription and even a receipt. But a few days later, when I went back to the site to browse content, I couldn’t get in. The site was down, and there was no way to contact anyone. I waited a few days, hoping it was just a technical issue. But then, I started doing some more research and realized that others had fallen victim to the same scam. The website had disappeared, and no one could find any trace of the company behind it. I was furious. I had just lost $39,000, and it seemed like there was no way to get it back. That's when I came across Folkwin Expert Recovery. They specialize in helping people recover funds from online scams like this. I was skeptical at first, but after reading reviews and seeing their success stories, I decided to give them a try. The team at Folkwin Expert Recovery was extremely professional. They asked for all the details about my transaction, including the payment method, and got to work right away. Within just a few days, I received updates from them, and eventually, they successfully recovered my $39,000. It felt like a huge weight was lifted off my shoulders. I honestly didn’t think it was possible to get my money back, but thanks to Folkwin Expert Recovery, I did. If you ever find yourself in a similar situation, I highly recommend reaching out to them. FOLKWINEXPERTRECOVERY(at)TECH-CENTER.C OM, TELEGRAM: @FOLKWIN_EXPERT_RECOVERY . They made the process simple and stress-free, and they delivered on their promises. Just remember to always be cautious when dealing with online subscriptions, especially if something feels too good to be true. Stay safe out there! Best Regards, Edward O. Elliott.

  • 11.04.25 08:10 Beatrice Gallagher

    I was defrauded of $78,000 by an individual I met online who was involved in a fraudulent investment endeavour. I initiated a search for legal assistance to retrieve my funds, and I encountered numerous testimonies regarding a criminal named RecoveryHacker101. I contacted them and provided the requisite information. The experts were able to locate and assist in the recovery of my misappropriated funds within approximately 36 hours. The fraudster was apprehended and apprehended by local authorities in his region, which is a source of immense relief for me. I trust that this information will be beneficial to the numerous individuals who have fallen victim to these fraudulent online investment scams. Their professional services are highly recommended for those in need of prompt and effective recovery assistance. If you require their services, you may only contact them via email at RecoveryHacker101[at]gmail[dot]com.

  • 13.04.25 01:13 michaeldavenport218

    I was recently scammed out of $53,000 by a fraudulent Bitcoin investment scheme, which added significant stress to my already difficult health issues, as I was also facing cancer surgery expenses. Desperate to recover my funds, I spent hours researching and consulting other victims, which led me to discover the excellent reputation of Capital Crypto Recover, I came across a Google post It was only after spending many hours researching and asking other victims for advice that I discovered Capital Crypto Recovery’s stellar reputation. I decided to contact them because of their successful recovery record and encouraging client testimonials. I had no idea that this would be the pivotal moment in my fight against cryptocurrency theft. Thanks to their expert team, I was able to recover my lost cryptocurrency back. The process was intricate, but Capital Crypto Recovery's commitment to utilizing the latest technology ensured a successful outcome. I highly recommend their services to anyone who has fallen victim to cryptocurrency fraud. For assistance, contact [email protected] Capital Crypto Recover on Telegram OR Call Number +1 (336)390-6684 via email: [email protected]

  • 13.04.25 01:13 michaeldavenport218

    I was recently scammed out of $53,000 by a fraudulent Bitcoin investment scheme, which added significant stress to my already difficult health issues, as I was also facing cancer surgery expenses. Desperate to recover my funds, I spent hours researching and consulting other victims, which led me to discover the excellent reputation of Capital Crypto Recover, I came across a Google post It was only after spending many hours researching and asking other victims for advice that I discovered Capital Crypto Recovery’s stellar reputation. I decided to contact them because of their successful recovery record and encouraging client testimonials. I had no idea that this would be the pivotal moment in my fight against cryptocurrency theft. Thanks to their expert team, I was able to recover my lost cryptocurrency back. The process was intricate, but Capital Crypto Recovery's commitment to utilizing the latest technology ensured a successful outcome. I highly recommend their services to anyone who has fallen victim to cryptocurrency fraud. For assistance, contact [email protected] Capital Crypto Recover on Telegram OR Call Number +1 (336)390-6684 via email: [email protected]

  • 14.04.25 23:44 elizabethrush89

    God bless Capital Crypto Recover Services for the marvelous work you did in my life, I have learned the hard way that even the most sensible investors can fall victim to scams. When my USD was stolen, for anyone who has fallen victim to one of the bitcoin binary investment scams that are currently ongoing, I felt betrayal and upset. But then I was reading a post on site when I saw a testimony of Wendy Taylor online who recommended that Capital Crypto Recovery has helped her recover scammed funds within 24 hours. after reaching out to this cyber security firm that was able to help me recover my stolen digital assets and bitcoin. I’m genuinely blown away by their amazing service and professionalism. I never imagined I’d be able to get my money back until I complained to Capital Crypto Recovery Services about my difficulties and gave all of the necessary paperwork. I was astounded that it took them 12 hours to reclaim my stolen money back. Without a doubt, my USDT assets were successfully recovered from the scam platform, Thank you so much Sir, I strongly recommend Capital Crypto Recover for any of your bitcoin recovery, digital funds recovery, hacking, and cybersecurity concerns. You reach them Call/Text Number +1 (336)390-6684 His Email: [email protected] Contact Telegram: @Capitalcryptorecover His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 17.04.25 03:56 tylerkevin

    I discovered CheapCrypto net while searching for a cryptocurrency trading platform that promised lower fees and better arbitrage opportunities than the well-known Binance. Intrigued by the potential for profit, I decided to take a leap of faith and exchanged approximately $45,700.567 worth of USDC for Ethereum. Initially, everything seemed to be going smoothly, and I felt optimistic about my investment.However, when I attempted to transfer my newly acquired Ethereum to my main crypto wallet, I encountered a significant problem. The website repeatedly displayed a message saying, "Trying again…" but my funds remained stuck on CheapCrypto net. As the minutes turned into hours, panic set in. I began to realize that I might have fallen victim to scammers.Desperate for a solution, I started researching ways to recover my lost funds. That’s when I came across DUNAMIS CYBER SOLUTION, a service that specializes in helping individuals recover lost or stolen cryptocurrency. Their reputation for assisting victims of scams and fraudulent platforms gave me a glimmer of hope. I reached out to them, explaining my situation and the challenges I faced with CheapCrypto net.The team at DUNAMIS CYBER SOLUTION was incredibly responsive and professional. They guided me through the process of documenting my transaction and provided me with the necessary steps to initiate a recovery request. Their expertise in dealing with similar cases was evident, and I felt reassured that I was in capable hands.Within a short period, Y DUNAMIS CYBER SOLUTION began their investigation into CheapCrypto net. They utilized advanced tracking techniques to trace the flow of my funds and identify the scammers behind the platform. Their thorough approach and commitment to helping me recover my lost assets were impressive.After a few days of diligent work, I received the fantastic news that DUNAMIS CYBER SOLUTION had successfully traced my Ethereum and was able to facilitate its return. I was overjoyed to have my $45,700.567 restored, and I couldn’t be more grateful for the assistance I received.This has taught me a valuable lesson about the importance of conducting thorough research before engaging with new trading platforms. While the allure of lower fees and arbitrage opportunities can be tempting, it’s crucial to prioritize security and reliability. Thanks to DUNAMIS CYBER SOLUTION, I was able to recover my funds and regain my peace of mind. I promised them that after recovering my assets, I would spread the good news to others who faced similar challenges, ensuring they know there is hope and DUNAMIS CYBER SOLUTION are available 24/7. +13433030545 [email protected] [email protected]

  • 18.04.25 20:39 michaeldavenport218

    I was recently scammed out of $53,000 by a fraudulent Bitcoin investment scheme, which added significant stress to my already difficult health issues, as I was also facing cancer surgery expenses. Desperate to recover my funds, I spent hours researching and consulting other victims, which led me to discover the excellent reputation of Capital Crypto Recover, I came across a Google post It was only after spending many hours researching and asking other victims for advice that I discovered Capital Crypto Recovery’s stellar reputation. I decided to contact them because of their successful recovery record and encouraging client testimonials. I had no idea that this would be the pivotal moment in my fight against cryptocurrency theft. Thanks to their expert team, I was able to recover my lost cryptocurrency back. The process was intricate, but Capital Crypto Recovery's commitment to utilizing the latest technology ensured a successful outcome. I highly recommend their services to anyone who has fallen victim to cryptocurrency fraud. For assistance, contact [email protected] Capital Crypto Recover on Telegram OR Call Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 18.04.25 20:39 michaeldavenport218

    I was recently scammed out of $53,000 by a fraudulent Bitcoin investment scheme, which added significant stress to my already difficult health issues, as I was also facing cancer surgery expenses. Desperate to recover my funds, I spent hours researching and consulting other victims, which led me to discover the excellent reputation of Capital Crypto Recover, I came across a Google post It was only after spending many hours researching and asking other victims for advice that I discovered Capital Crypto Recovery’s stellar reputation. I decided to contact them because of their successful recovery record and encouraging client testimonials. I had no idea that this would be the pivotal moment in my fight against cryptocurrency theft. Thanks to their expert team, I was able to recover my lost cryptocurrency back. The process was intricate, but Capital Crypto Recovery's commitment to utilizing the latest technology ensured a successful outcome. I highly recommend their services to anyone who has fallen victim to cryptocurrency fraud. For assistance, contact [email protected] Capital Crypto Recover on Telegram OR Call Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 19.04.25 02:00 [email protected]

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  • 20.04.25 00:45 khouser

    Greetings, Katrina from Georgia. I would like to sincerely thank Supreme Peregrine Recovery for their assistance in repairing and improving my credit score. When I initially contacted them, I was confused about how to raise my credit score and feeling overburdened by my financial circumstances. Their staff helped me every step of the way and was very informed and helpful. In addition to helping me comprehend my credit report and offering helpful advice for money management, they also developed customized plans to deal with my credit problems. Within a few months, I noticed a notable improvement in my credit score because of their knowledge. I can now confidently pursue my ambitions and feel more secure about my financial future. +1,8,7,0,2,2,6,0,6,5,9 supremeperegrinerecovery567(@)zohomail(.)com supremeperegrinerecovery(@)proton(.)me info(@)supremeperegrinerecovery(.)com

  • 20.04.25 17:22 patricialovick86

    How To Recover Your Bitcoin Without Falling Victim To Scams: A  Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact: [email protected] 

  • 20.04.25 17:22 patricialovick86

    How To Recover Your Bitcoin Without Falling Victim To Scams: A  Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 21.04.25 03:51 gleerandon

    Lost, Stolen, or Scammed Crypto Asset Recovery Services For Hire - Contact Dune Nectar Web Expert. The process of recovering lost cryptocurrency assets for victims of fraudulent schemes has presented significant challenges. Individuals who have been defrauded through social media platforms, including Instagram and Telegram, and deceptive investment websites often encounter difficulties in identifying legitimate crypto recovery companies capable of assisting in retrieving their lost investments. The consequences of falling victim to such scams can be profoundly detrimental, extending beyond mere financial loss. The emotional and psychological impact can be severe, potentially leading to significant stress, the accumulation of debt, and even legal complications. In extreme cases, the distress caused by fraudulent activities has been linked to instances of suicide among victims. Given cryptocurrency fraud's multifaceted and potentially devastating repercussions, victims must seek appropriate assistance. Should an individual find themselves in the unfortunate position of having been scammed or having had their cryptocurrency stolen, it is strongly recommended that they contact the DuneNectarWebExpert recovery team. This team specializes in providing support and guidance to individuals seeking to recover their lost funds. To get assistance, victims are advised to file a detailed complaint to DuneNectarWebExpert team via [ Support @Dunenectarwebexpert . com. ] or Telegram [ DuneNectarWebExpert ]. This complaint should include all available evidence related to the fraudulent activity, such as transaction records, communication logs, and any other pertinent documentation. Upon receipt of the complaint and supporting evidence, DuneNectarWebExpert team will commence the necessary procedures to facilitate the recovery of the lost cryptocurrency assets.

  • 21.04.25 12:19 michaeldavenport218

    I was recently scammed out of $53,000 by a fraudulent Bitcoin investment scheme, which added significant stress to my already difficult health issues, as I was also facing cancer surgery expenses. Desperate to recover my funds, I spent hours researching and consulting other victims, which led me to discover the excellent reputation of Capital Crypto Recover, I came across a Google post It was only after spending many hours researching and asking other victims for advice that I discovered Capital Crypto Recovery’s stellar reputation. I decided to contact them because of their successful recovery record and encouraging client testimonials. I had no idea that this would be the pivotal moment in my fight against cryptocurrency theft. Thanks to their expert team, I was able to recover my lost cryptocurrency back. The process was intricate, but Capital Crypto Recovery's commitment to utilizing the latest technology ensured a successful outcome. I highly recommend their services to anyone who has fallen victim to cryptocurrency fraud. For assistance, contact [email protected] Capital Crypto Recover on Telegram OR Call Number +1 (336)390-6684 via email: [email protected]

  • 24.04.25 17:59 cynthia19morris

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  • 25.04.25 15:44 Sharo2025

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  • 03.05.25 05:01 melissaholroyd

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  • 14.05.25 14:45 Clarkanderson

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  • 16.05.25 14:18 patricialovick86

    How To Recover Your Bitcoin Without Falling Victim To Scams: A  Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 16.05.25 14:18 patricialovick86

    How To Recover Your Bitcoin Without Falling Victim To Scams: A  Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 17.05.25 18:33 marywilliam3544

    A few months ago, I became a victim of a crypto scam that cost me more than $42,000. It started with what looked like a legitimate investment opportunity on social media. The platform was well-designed, the “advisors” sounded experienced, and the returns they promised seemed realistic at the time. I did some quick research, saw fake positive reviews, and decided to give it a try.At first, everything seemed to go smoothly. I deposited small amounts and saw returns in my account almost immediately. Encouraged, I added more—until I realized I could no longer withdraw anything. The site shut down, the contact numbers went dead, and the people I had spoken to disappeared. That’s when it hit me—I had been scammed.I was embarrassed, angry, and honestly, heartbroken. I didn’t think there was any way to get the money back. My bank couldn’t help, the police didn’t have any tools for crypto tracing, and I felt completely stuck. Then, a friend referred me to PRO WIZARD GILBERT RECOVERY. I was hesitant at first, but after speaking with one of their recovery specialists, I felt a sense of hope I hadn’t felt in weeks. They were incredibly professional, didn’t make any exaggerated claims, and explained their process clearly.The team began working right away using advanced blockchain forensics to trace the stolen funds. Within a few days, they located the wallets that received my funds and started the legal steps necessary to flag and recover the crypto. I was blown away by how thorough and efficient they were After several weeks of careful investigation and coordination, PRO WIZARD GILBERT RECOVERY successfully recovered nearly 75% of my lost funds. I couldn’t believe it. I went from thinking that money was gone forever to having it returned to me—and all thanks to their dedication and expertise.If you’ve lost money to a crypto scam, I can’t recommend PRO WIZARD GILBERT RECOVERY enough. They’re the real deal. Professional, honest, and relentless in fighting for their clients. Thanks to them, I’ve not only recovered most of what I lost, but I’ve also regained peace of mind. CONTACT INFO=====WhatsApp +1 (920) 408‑1234 TELEGRAM====== http s:// t. me/Pro_Wizard_Gilbert_Recovery EMAIL========== pro wizard gilbert recovery (@) engineer. com

  • 19.05.25 05:42 kylebro

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  • 20.05.25 11:40 robertalfred175

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  • 20.05.25 11:40 robertalfred175

    CRYPTO SCAM RECOVERY SUCCESSFUL – A TESTIMONIAL OF LOST PASSWORD TO YOUR DIGITAL WALLET BACK. My name is Robert Alfred, Am from Australia. I’m sharing my experience in the hope that it helps others who have been victims of crypto scams. A few months ago, I fell victim to a fraudulent crypto investment scheme linked to a broker company. I had invested heavily during a time when Bitcoin prices were rising, thinking it was a good opportunity. Unfortunately, I was scammed out of $120,000 AUD and the broker denied me access to my digital wallet and assets. It was a devastating experience that caused many sleepless nights. Crypto scams are increasingly common and often involve fake trading platforms, phishing attacks, and misleading investment opportunities. In my desperation, a friend from the crypto community recommended Capital Crypto Recovery Service, known for helping victims recover lost or stolen funds. After doing some research and reading multiple positive reviews, I reached out to Capital Crypto Recovery. I provided all the necessary information—wallet addresses, transaction history, and communication logs. Their expert team responded immediately and began investigating. Using advanced blockchain tracking techniques, they were able to trace the stolen Dogecoin, identify the scammer’s wallet, and coordinate with relevant authorities to freeze the funds before they could be moved. Incredibly, within 24 hours, Capital Crypto Recovery successfully recovered the majority of my stolen crypto assets. I was beyond relieved and truly grateful. Their professionalism, transparency, and constant communication throughout the process gave me hope during a very difficult time. If you’ve been a victim of a crypto scam, I highly recommend them with full confidence contacting: Email: [email protected] Telegram: @Capitalcryptorecover Call/Text: +1 (336) 390-6684 Website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 26.05.25 17:55 Juliuslaurence1

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  • 30.05.25 05:03 kevinpatmore2

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  • 01.06.25 17:55 springthorpecameron5

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  • 02.06.25 16:01 wendytaylor015

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  • 02.06.25 16:01 wendytaylor015

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  • 03.06.25 22:21 [email protected]

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  • 06.06.25 18:43 jack67667766

    Jasmine Lopez is an expert in retrieving stolen cryptocurrency, including Ethereum and USDT. Her effective methods make her a reliable ally for theft victims. One client, who lost €908,000, sought her assistance, and Jasmine managed to recover the full amount within a day, bringing immense relief to the client. Jasmine is dedicated to helping others in similar situations and is available to offer support. For help with recovering lost funds, you can contact her via email at [email protected] or on WhatsApp at ‪+44 736 644 5035‬.

  • 08.06.25 12:49 jack67667766

    Jasmine Lopez es una experta en recuperar criptomonedas robadas, como Ethereum y USDT. Ella usa métodos efectivos que la hacen una buena ayuda para quienes han sido víctimas de robo. Un cliente que perdió 908 mil euros acudió a ella, y en un día, Jasmine logró devolverle toda la cantidad. Esto trajo gran alivio al cliente. Ella tiene como objetivo ayudar a otros en situaciones similares y está lista para ofrecer apoyo. Si necesitas ayuda para recuperar fondos perdidos, puedes contactarla por correo electrónico en [email protected] o por WhatsApp al número ‪+44 736 644 5035‬.

  • 09.06.25 19:49 garnierroux

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  • 21.06.25 04:37 jamesgrant

    The emergence of cryptocurrencies has revolutionized the financial landscape, yet it has also given rise to significant challenges, particularly concerning security and the potential for loss of assets. In this context, individuals often seek assistance from entities called SCANNER HACKER CRYPTO RECOVERY, which purport to employ sophisticated techniques to reclaim lost Bitcoin (BTC) from compromised wallets or exchanges. However, while the allure of recovering lost assets can be compelling, it is imperative to approach these services with a critical lens. The cryptocurrency ecosystem is rife with scams and fraudulent schemes, ranging from phishing attacks to outright theft; thus, due diligence is paramount. Scholars and practitioners in the field must advocate for more robust security measures, educate stakeholders on the inherent risks of cryptocurrency ownership, and promote best practices in digital asset management to mitigate the likelihood of loss. Furthermore, effective policymaking to regulate these recovery services, hold malicious actors accountable, and protect consumers is essential to fostering a safer environment in the rapidly evolving world of digital currencies. You can communicate with SCANNER HACKER CRYPTO RECOVERY Via Email: [email protected] Web: https://scannerhacktech.com/ Whatsapp: +1 431 801 7493

  • 23.06.25 15:44 michaeldavenport218

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  • 23.06.25 15:44 michaeldavenport218

    I was recently scammed out of $53,000 by a fraudulent Bitcoin investment scheme, which added significant stress to my already difficult health issues, as I was also facing cancer surgery expenses. Desperate to recover my funds, I spent hours researching and consulting other victims, which led me to discover the excellent reputation of Capital Crypto Recover, I came across a Google post It was only after spending many hours researching and asking other victims for advice that I discovered Capital Crypto Recovery’s stellar reputation. I decided to contact them because of their successful recovery record and encouraging client testimonials. I had no idea that this would be the pivotal moment in my fight against cryptocurrency theft. Thanks to their expert team, I was able to recover my lost cryptocurrency back. The process was intricate, but Capital Crypto Recovery's commitment to utilizing the latest technology ensured a successful outcome. I highly recommend their services to anyone who has fallen victim to cryptocurrency fraud. For assistance, contact [email protected] Capital Crypto Recover on Telegram OR Call Number +1 (336)390-6684 via email: [email protected] you can visit his website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 24.06.25 04:10 Beth Wilson

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  • 24.06.25 04:12 Beth Wilson

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  • 24.06.25 04:18 Beth Wilson

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  • 24.06.25 04:23 Beth Wilson

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  • 25.06.25 22:56 rennebrandon

    I am forever grateful to the amazing team at Dune Nectar Web Expert. They did what I thought was never possible. They played a crucial role in helping me recover all my lost funds from a fraudulent forex and crypto trading scheme, including the pråofits I thought I'd earned. Looking back, I realize I was a bit of a fool for trusting greedy and deceitful brokers with my hard-earned money. However, I'm overjoyed that I found Dune Nectar Web Expert. They are a team of honest and highly skilled professionals available for hire. Dune Nectar Web Expert helps individuals and organizations recover stolen cryptocurrencies and digital assets. They helped me heal every penny I lost and provided me with the right signals and a reliable platform to trade with. Thanks to Dune Nectar Web Expert, I'm earning more than ever, and I couldn't be happier. That's why I can't stop sharing my positive experience and praising their amazing services and expertise. If you're still struggling with failures in binary options, crypto, or forex trading, or if you're looking to recover your lost USDC, Bitcoin, Ethereum, or other crypto funds, I strongly advise you to reach out to: Telegram>>> ( T.me/dunenectarwebexpert ) Mail>>>> Support (@) Dunenectarwebexpert (.) Com Web>>> https://dunenectarwebexpert.com/

  • 26.06.25 20:33 paulmargaret

    Dear Wizard Hilton Cyber Tech Team, I am writing to express my heartfelt gratitude and appreciation for your exceptional service in recovering my scammed funds. After falling victim to a scam and experiencing numerous disappointments, I was amazed by your team's professionalism, expertise, and dedication to helping me retrieve my lost money. Your prompt response and efficient handling of my case were truly impressive. Within 24 hours, you successfully recovered my funds, and I was overjoyed to see the money safely returned to my account. Your team's commitment to helping individuals like me, who have been scammed, is truly commendable. Your work not only restored my financial security but also gave me peace of mind and renewed trust in the digital world. I would like to highly recommend your services to anyone who has been a victim of scams or cybercrime. Your expertise and support can make a significant difference in recovering lost funds and navigating complex digital situations. Thank you again for your outstanding work and dedication. I am grateful for your help and wish you continued success in your endeavors     Email : wizardhiltoncybertech ( @ ) gmail (. ) com OR support ( @ ) wizardhiltoncybertech (.) com WhatsApp number +18737715701 . Sincerely, Kimberly Williams

  • 27.06.25 00:46 paulmargaret

    Dear Wizard Hilton Cyber Tech Team, I am writing to express my heartfelt gratitude and appreciation for your exceptional service in recovering my scammed funds. After falling victim to a scam and experiencing numerous disappointments, I was amazed by your team's professionalism, expertise, and dedication to helping me retrieve my lost money. Your prompt response and efficient handling of my case were truly impressive. Within 24 hours, you successfully recovered my funds, and I was overjoyed to see the money safely returned to my account. Your team's commitment to helping individuals like me, who have been scammed, is truly commendable. Your work not only restored my financial security but also gave me peace of mind and renewed trust in the digital world. I would like to highly recommend your services to anyone who has been a victim of scams or cybercrime. Your expertise and support can make a significant difference in recovering lost funds and navigating complex digital situations. Thank you again for your outstanding work and dedication. I am grateful for your help and wish you continued success in your endeavors     Email : wizardhiltoncybertech ( @ ) gmail (. ) com OR support ( @ ) wizardhiltoncybertech (.) com WhatsApp number +18737715701 . Sincerely, Kimberly Williams

  • 27.06.25 22:31 rennebrandon

    I am forever grateful to the amazing team at Dune Nectar Web Expert. They did what I thought was never possible. They played a crucial role in helping me recover all my lost funds from a fraudulent forex and crypto trading scheme, including the pråofits I thought I'd earned. Looking back, I realize I was a bit of a fool for trusting greedy and deceitful brokers with my hard-earned money. However, I'm overjoyed that I found Dune Nectar Web Expert. They are a team of honest and highly skilled professionals available for hire. Dune Nectar Web Expert helps individuals and organizations recover stolen cryptocurrencies and digital assets. They helped me heal every penny I lost and provided me with the right signals and a reliable platform to trade with. Thanks to Dune Nectar Web Expert, I'm earning more than ever, and I couldn't be happier. That's why I can't stop sharing my positive experience and praising their amazing services and expertise. If you're still struggling with failures in binary options, crypto, or forex trading, or if you're looking to recover your lost USDC, Bitcoin, Ethereum, or other crypto funds, I strongly advise you to reach out to: Telegram>>> ( T.me/dunenectarwebexpert ) Mail>>>> Support (@) Dunenectarwebexpert (.) Com Web>>> https://dunenectarwebexpert.com/

  • 28.06.25 00:46 patricialovick86

    How To Recover Your Bitcoin Without Falling Victim To Scams: A  Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 28.06.25 00:46 patricialovick86

    How To Recover Your Bitcoin Without Falling Victim To Scams: A  Testimony Experience With Capital Crypto Recover Services, Contact Telegram: @Capitalcryptorecover Dear Everyone, I would like to take a moment to share my positive experience with Capital Crypto Recover Services. Initially, I was unsure if it would be possible to recover my stolen bitcoins. However, with their expertise and professionalism, I was able to fully recover my funds. Unfortunately, many individuals fall victim to scams in the cryptocurrency space, especially those involving fraudulent investment platforms. However, I advise caution, as not all recovery services are legitimate. I personally lost $273,000 worth of Bitcoin from my Binance account due to a deceptive platform. If you have suffered a similar loss, you may be considering crypto recovery, The Capital Crypto Recover is the most knowledgeable and effective Capital Crypto Recovery Services assisted me in recovering my stolen funds within 24 hours, after getting access to my wallet. Their service was not only prompt but also highly professional and effective, and many recovery services may not be trustworthy. Therefore, I highly recommend Capital Crypto Recover to you. i do always research and see reviews about their service, For assistance finding your misplaced cryptocurrency, get in touch with them, They do their jobs quickly and excellently, Stay safe and vigilant in the crypto world. You can reach them via email at [email protected] OR Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 29.06.25 07:39 paulmargaret

    Dear Wizard Hilton Cyber Tech Team, I am writing to express my heartfelt gratitude and appreciation for your exceptional service in recovering my scammed funds. After falling victim to a scam and experiencing numerous disappointments, I was amazed by your team's professionalism, expertise, and dedication to helping me retrieve my lost money. Your prompt response and efficient handling of my case were truly impressive. Within 24 hours, you successfully recovered my funds, and I was overjoyed to see the money safely returned to my account. Your team's commitment to helping individuals like me, who have been scammed, is truly commendable. Your work not only restored my financial security but also gave me peace of mind and renewed trust in the digital world. I would like to highly recommend your services to anyone who has been a victim of scams or cybercrime. Your expertise and support can make a significant difference in recovering lost funds and navigating complex digital situations. Thank you again for your outstanding work and dedication. I am grateful for your help and wish you continued success in your endeavors     Email : wizardhiltoncybertech ( @ ) gmail (. ) com OR support ( @ ) wizardhiltoncybertech (.) com WhatsApp number +18737715701 . Sincerely, Kimberly Williams

  • 29.06.25 11:52 wendytaylor015

    My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

  • 30.06.25 15:06 wendytaylor015

    My name is Wendy Taylor, I'm from Los Angeles, i want to announce to you Viewer how Capital Crypto Recover help me to restore my Lost Bitcoin, I invested with a Crypto broker without proper research to know what I was hoarding my hard-earned money into scammers, i lost access to my crypto wallet or had your funds stolen? Don’t worry Capital Crypto Recover is here to help you recover your cryptocurrency with cutting-edge technical expertise, With years of experience in the crypto world, Capital Crypto Recover employs the best latest tools and ethical hacking techniques to help you recover lost assets, unlock hacked accounts, Whether it’s a forgotten password, Capital Crypto Recover has the expertise to help you get your crypto back. a security company service that has a 100% success rate in the recovery of crypto assets, i lost wallet and hacked accounts. I provided them the information they requested and they began their investigation. To my surprise, Capital Crypto Recover was able to trace and recover my crypto assets successfully within 24hours. Thank you for your service in helping me recover my $647,734 worth of crypto funds and I highly recommend their recovery services, they are reliable and a trusted company to any individuals looking to recover lost money. Contact email [email protected] OR Telegram @Capitalcryptorecover Call/Text Number +1 (336)390-6684 his contact: [email protected] His website: https://recovercapital.wixsite.com/capital-crypto-rec-1

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